Do Generative Models Keep Time? A Time-Aware Evaluation of Synthetic Sequential Tabular Data

# Do Generative Models Keep Time? A Time-Aware Evaluation of Synthetic Sequential Tabular Data
Source: [https://arxiv.org/html/2607.15606](https://arxiv.org/html/2607.15606)
\(2026\)

###### Abstract\.

Synthetic sequential tabular data are increasingly used for privacy\-preserving data sharing, yet a generator can reproduce every marginal and every foreign\-key relationship while emitting timestamps that run backwards or repeat, and while sending entities along paths that no real entity followed\. Conventional tabular evaluation, which pools records into static distributions, is blind to such failures\. We present a taxonomy\-guided evaluation protocol for temporal fidelity, in which the applicable measurements are determined by the data rather than fixed in advance\. Each dataset is first characterized along four properties — how time is represented, whether observations are regularly sampled, whether trajectories are mutually dependent, and how the schema links entities to their histories — and these properties determine which evaluation dimensions are meaningful\. The protocol then measures timestamp validity, cross\-sectional structure at aligned time points, within\-entity dynamics, and time\-varying relational structure, and recasts utility and privacy evaluation over trajectories rather than isolated rows\. We apply the protocol to eight generative models across thirteen datasets spanning six domains\. Rankings under conventional evaluation disagree substantially with those obtained under temporal evaluation, and the resulting failures are architecture\-coherent rather than random\. Temporal fidelity must therefore be measured on the time axis itself, rather than inferred from pooled record distributions\.

synthetic data, sequential tabular data, temporal fidelity, benchmark, generative models, relational data

Preprint\.

††journalyear:2026††ccs:Computing methodologies Data generation and augmentation††ccs:Mathematics of computing Time series analysis††ccs:Hardware Evaluation## 1\.Introduction

The demand for synthetic tabular data has grown rapidly in domains such as finance\(Potluruet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib32); Assefaet al\.,[2020](https://arxiv.org/html/2607.15606#bib.bib33)\)and healthcare\(Rankinet al\.,[2020](https://arxiv.org/html/2607.15606#bib.bib34)\), driven by privacy regulations and limited access to sensitive records\(Ntoutsiet al\.,[2020](https://arxiv.org/html/2607.15606#bib.bib30); Rajpurkaret al\.,[2022](https://arxiv.org/html/2607.15606#bib.bib31)\)\. Sequential tabular data — in which timestamped records accumulate over time and are grouped by a persistent entity such as a customer, patient, or account\(Zhanget al\.,[2022b](https://arxiv.org/html/2607.15606#bib.bib49)\)— is in fact the dominant data format across many high\-stakes domains: transaction logs in finance, visit records in healthcare, usage histories in retail, and sensor streams in industrial systems all share this structure\. Despite its ubiquity, the synthesis and evaluation of such data remain critical yet underexplored\.

Existing evaluation frameworks overlook the temporal structure of such data\. Single\-table benchmarks\(Qianet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib24); Lautrupet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib23)\)treat records as independent samples, while relational benchmarks\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22); Robinsonet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib25)\)evaluate inter\-table dependencies but remain agnostic to temporal ordering and population dynamics\. Prior work targeting sequential tabular data\(Zhanget al\.,[2022b](https://arxiv.org/html/2607.15606#bib.bib49); Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)relies on aggregate\-level similarity, leaving cross\-sectional dynamics and trajectory\-level fidelity unaddressed\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x1.png)Figure 1\.Motivation for temporal fidelity evaluation\. \(a\) Synthetic data may appear similar to real data when evaluated only by marginal distributions\. However, temporal views reveal mismatches in \(b\) timestamp fidelity, \(c\) cross\-sectional distributions across time, and \(d\) trajectory\-level evolution\.A four\-panel motivation figure showing why marginal distribution matching is insufficient for evaluating temporal synthetic data\. Panel \(a\) shows that real and synthetic data can have nearly overlapping marginal distributions, even though a warning box states that marginal distributions may not be enough to explain the data\. Panel \(b\) illustrates timestamp fidelity problems, where synthetic sequences contain duplicate timestamps and missing timestamps compared with regular real timestamp sequences\. Panel \(c\) compares real and synthetic customer values over calendar time and highlights discrepancies in cross\-sectional distributions\. Panel \(d\) compares real and synthetic trajectory\-level customer trends over time and highlights first\-difference misalignment and trajectory\-level distribution discrepancies\. Overall, the figure shows that temporal mismatches can remain hidden under marginal\-distribution evaluation but become visible through timestamp, cross\-sectional, and trajectory\-level fidelity views\.Figure[1](https://arxiv.org/html/2607.15606#S1.F1)illustrates the consequences of this gap\. ClavaDDPM\(Panget al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib7)\), a state\-of\-the\-art relational generative model produces synthetic records that violate chronological order and contain duplicate timestamps, which is incompatible with the constraints of real\-world sequential data\. However, they are not detected by existing benchmarks: the synthetic data attains near\-perfect marginal fidelity on Rossmann \(a\), as conventional metrics collapse temporal structure into static distributions\. The discrepancy emerges under timestamp \(b\), cross\-sectional \(c\), and trajectory\-level \(d\) inspection where the synthetic population fails to reflect real\-world temporal dynamics\.

To address this limitation, we introduceSeq2Synth, a unified benchmark for evaluating temporal fidelity in synthetic sequential tabular data\. The central claim of this paper is that temporal fidelity cannot be reliably inferred from static or relational fidelity: a generator may match marginal or relational distributions while violating temporal order, distorting population dynamics, corrupting within\-entity evolution, or breaking time\-varying relational structure\. Seq2Synth operationalizes this claim by mapping dataset characteristics to applicable evaluation dimensions and by measuring four complementary forms of temporal fidelity: timestamp validity, cross\-sectional fidelity, longitudinal fidelity, and structural consistency\. We further extend standard utility and privacy protocols to trajectory\-aware settings, so that downstream usefulness and leakage risk are evaluated under sequential dependencies rather than row\-level similarity alone\.

Contributions\.\(1\)We formulate a taxonomy\-guided evaluation protocol for sequential tabular data, where time representation, sampling regularity, cross\-trajectory dependence, and schema structure determine which temporal metrics are applicable\.\(2\)We instantiate this protocol inSeq2Synth, covering timestamp, cross\-sectional, longitudinal, and structural fidelity, with trajectory\-aware utility and privacy extensions\.\(3\)We build a 13\-dataset benchmark across six domains and evaluate eight representative generators, showing that static\-distribution rankings disagree substantially with temporal\-aware rankings and that different architectures fail along distinct temporal dimensions\.

## 2\.Related Work

##### Synthetic Tabular Data Generation

Synthetic data generation has been studied through several approaches\. Early relational synthesis methods, such as SDV\(Patkiet al\.,[2016](https://arxiv.org/html/2607.15606#bib.bib10)\)and RCTGAN\(Gueyeet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib11)\), relied on hierarchical or conditional generation, while ClavaDDPM\(Panget al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib7)\)incorporated inter\-table relationships into diffusion\. Recent graph\-based methods, including RGCLD\(Hudovernik,[2024](https://arxiv.org/html/2607.15606#bib.bib12)\)and RelDiff\(Hudoverniket al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib8)\), use GNNs to model structural dependencies and improve relational consistency\. RDB\-Diffusion\(Ketataet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib14)\)applies structure\-aware diffusion to preserve intra\-table distributions and inter\-table consistency at scale\. Meanwhile, the Synthetic Data Vault \(SDV\) library\(DataCebo, Inc\.,[2020](https://arxiv.org/html/2607.15606#bib.bib51)\)supports sequential tabular data through CPAR\(Zhanget al\.,[2022a](https://arxiv.org/html/2607.15606#bib.bib16)\), which, along with TabularARGN\(Tiwaldet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib15)\), uses autoregressive modeling in single\-table settings\. REaLTabFormer\(Solatorio and Dupriez,[2023](https://arxiv.org/html/2607.15606#bib.bib9)\)\(RTF\) employs a Seq2Seq\-based framework for linear schemas linking parent entities to child trajectory tables\. Relevant to our benchmark, TabDiT\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)adopts an autoregressive diffusion Transformer for time\-dependent relational data, covering the broadest range of sequential tabular structures among existing methods\.

##### Evaluation for Synthetic Data

Various benchmark frameworks have been developed to measure synthetic data quality across modalities\. SynthCity\(Qianet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib24)\)and SynthEval\(Lautrupet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib23)\)provide tools to assess fidelity, utility, and privacy\. For relational data, specialized frameworks account for cross\-table dependencies and structural consistency: RelBench\(Robinsonet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib25)\)evaluates utility by transforming tabular records into graph structures and applying graph neural networks to downstream prediction tasks, while SyntheRela\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\)measures relational fidelity by aggregating child\-table features into parent tables before conducting classifier\-based two\-sample tests\. The SDV library\(Patkiet al\.,[2016](https://arxiv.org/html/2607.15606#bib.bib10)\)provides evaluation metrics \(e\.g\., SDMetrics\) that can capture step\-wise distributional similarities for sequential data\. Models targeting sequential tabular data evaluate temporal characteristics using model\-specific metrics\. TabDiT\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)reports MLD\-TS and MLE\-TS, while TabularARGN\(Tiwaldet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib15)\)employs a coherence metric based on successive time\-step pairs\. However, these evaluations for sequential tabular data lack a unified and systematic framework for evaluating temporal characteristics across diverse sequential structures, allowing critical failure modes in state\-of\-the\-art models to remain undetected\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x2.png)Figure 2\.Overview of proposed temporal fidelity evaluation metrics\.Timestamp Fidelitydetects temporal violations\.Cross\-Sectional Fidelitycaptures distribution differences at each time step\.Longitudinal Fidelitycompares step\-level differences and global trajectory differences\.Structural Fidelitychecks similarity in table relationship\.An overview figure of the proposed temporal fidelity evaluation metrics, organized into four columns\. The timestamp column illustrates three types of timestamp violations: duplicated timestamps, missing grid points, and timestamps outside the valid range\. The cross\-sectional column shows distributions compared at each time step, with real and synthetic values forming different per\-time distributions\. The longitudinal column shows two trajectory\-based comparisons: step\-level differences between consecutive time points and trajectory\-level differences across entire sequences\. The structural column shows parent\-child table relationships and compares relational cardinality distributions between real and synthetic data\.

## 3\.Seq2Synth Benchmark

Table 1\.Comparison of existing evaluation frameworks for synthetic tabular data\.✓: explicitly supported,△\\triangle: partially or indirectly supported, ✗: not explicitly addressed\.A comparison table of existing evaluation frameworks for synthetic tabular data\. Rows indicate evaluation dimensions, including timestamp validity, cross\-sectional dynamics, longitudinal trajectory dynamics, relational or structural fidelity, temporal utility, and temporal privacy\. Columns group existing frameworks into single\-table benchmarks, relational\-table benchmarks, sequential tabular generative models, and the proposed framework\. Most existing frameworks address only a subset of these dimensions, while the proposed framework supports all six\.Evaluation dimensionSingle\-tableRelationalSequentialOursSynthCity\(Qianet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib24)\)SynthEval\(Lautrupet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib23)\)SynMeter\(Du and Li,[2025](https://arxiv.org/html/2607.15606#bib.bib50)\)RelBench\(Robinsonet al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib25)\)SyntheRela\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\)SDV\(DataCebo, Inc\.,[2020](https://arxiv.org/html/2607.15606#bib.bib51)\)TabularARGN\(Tiwaldet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib15)\)TabDiT\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)\\columncolorblue\!7Seq2SynthTimestamp validity✗✗✗✗✗✗✗✗\\columncolorblue\!7✓Cross\-sectional dynamics✗✗✗✗✗✗✗✗\\columncolorblue\!7✓Trajectory dynamics✗✗✗✗✗✓△\\triangle✓\\columncolorblue\!7✓Structural fidelity✗✗✗✓✓✓✗✗\\columncolorblue\!7✓Temporal utility✗✗✗✗✗✗✓✓\\columncolorblue\!7✓Temporal privacy✗✗✗✗✗✗✗✗\\columncolorblue\!7✓

To address the limitations of existing frameworks \(See Table[1](https://arxiv.org/html/2607.15606#S3.T1)\.\), Seq2Synth evaluates synthetic sequential tabular data through a taxonomy\-guided protocol rather than a fixed list of universally applied metrics\. Given a real relational dataset𝒯\\mathcal\{T\}and a synthetic counterpart𝒯^\\hat\{\\mathcal\{T\}\}, the benchmark first identifies the temporal and structural properties of the data, selects the applicable evaluation dimensions, normalizes metric inputs when required, and reports fidelity, utility, and privacy scores under this common protocol\.

### 3\.1\.Data Model and Taxonomy

Real\-world data such as customer transaction histories and patient visit records share a common structure: timestamped records accumulate over time and are grouped by a persistent entity\. We define this class assequential tabular data\. Let𝒯=\{T1,…,TD\}\\mathcal\{T\}=\\\{T\_\{1\},\\ldots,T\_\{D\}\\\}denote a relational dataset with temporal and referential dependencies, and letT∈𝒯T\\in\\mathcal\{T\}be a target table containingNNtimestamped records:

T=\{\(xik​e​y,xit​i​m​e,𝒓i\)\}i=1N,T=\\\{\(x^\{key\}\_\{i\},\\,x^\{time\}\_\{i\},\\,\{\\bm\{r\}\}\_\{i\}\)\\\}\_\{i=1\}^\{N\},wherexik​e​yx^\{key\}\_\{i\}identifies the entity,xit​i​m​e∈Ωx^\{time\}\_\{i\}\\in\\Omegais its timestamp, and𝒓i=\(𝒙in​u​m,𝒙ic​a​t\)\{\\bm\{r\}\}\_\{i\}=\(\{\\bm\{x\}\}^\{num\}\_\{i\},\{\\bm\{x\}\}^\{cat\}\_\{i\}\)contains numerical and categorical attributes\. For each entitykk, the rows withxik​e​y=kx^\{key\}\_\{i\}=k, ordered by timestamp, form a trajectory

T​\(k\)=\{\(xk,jt​i​m​e,𝒓k,j\)\}j=1Lk,xk,1t​i​m​e≤⋯≤xk,Lkt​i​m​e\.T\(k\)=\\\{\(x^\{time\}\_\{k,j\},\\,\{\\bm\{r\}\}\_\{k,j\}\)\\\}\_\{j=1\}^\{L\_\{k\}\},\\qquad x^\{time\}\_\{k,1\}\\leq\\cdots\\leq x^\{time\}\_\{k,L\_\{k\}\}\.
##### Taxonomy

Seq2Synth classifies each dataset along four axes that determine which metrics are meaningful: \(1\)time representation, distinguishing absolute calendar time from relative per\-trajectory time; \(2\)sampling regularity, distinguishing regular grids from irregular event intervals; \(3\)trajectory dependence, distinguishing population\-level dependent trajectories from isolated entities; and \(4\)schema structure, distinguishing single, linear, multi\-child, and multi\-parent schemas\.111Singleschemas reside in one table where time\-invariant attributes are implicit in the entity identifier, whilelinearschemas separate them into one parent table linked to a child trajectory table\.The taxonomy\-to\-metric mapping is summarized in Table[9](https://arxiv.org/html/2607.15606#A0.T9); definitions are in Online Appendix B\.

### 3\.2\.Benchmark Protocol

Seq2Synth follows four steps\.

##### Step 1: classify the dataset

The dataset is first assigned to the taxonomy above, which determines whether aligned population\-level, grid\-based, and relational\-structure evaluations are applicable\.

##### Step 2: select applicable dimensions

The benchmark then selects among four temporal fidelity dimensions\.TimestampandLongitudinalfidelity apply broadly because they evaluate the time axis and within\-entity trajectories\.Cross\-sectionalfidelity requires absolute time and dependent trajectories, since it compares population distributions at aligned time points\.Structuralfidelity is selected according to the schema axis, with additional metrics for multi\-child and multi\-parent schemas\.

##### Step 3: normalize metric inputs

Timestamp metrics are computed on raw generator outputs so that invalid order, duplicate timestamps, out\-of\-range timestamps, and missing grid points are not hidden by repair\. Non\-timestamp metrics require well\-defined temporal inputs, so Seq2Synth applies a post\-processing pipeline before computing cross\-sectional, longitudinal, and structural scores: records are sorted, timestamps are aligned when a grid is defined, out\-of\-range records are trimmed, duplicate entity–timestamp pairs are resolved, and regular\-series gaps are imputed\. We use the sparse variant as the default for cross\-sectional and structural metrics, because leaving missing grid points as NaN exposes temporal coverage failures; longitudinal trajectory metrics use the interpolation\-fill variant when complete trajectories are required\. Full pipeline details and imputation ablations are in Online Appendix C\.

##### Step 4: report dimension\-level scores

Each metric produces a score in a common orientation, where higher is better except for reported distances\. Scores are aggregated within each dimension over metrics applicable to each dataset\. This design prevents inapplicable temporal assumptions from being imposed on datasets with different time representations, sampling patterns, or schema structures\.

### 3\.3\.Temporal Fidelity Dimensions

Figure[2](https://arxiv.org/html/2607.15606#S2.F2)summarizes the four fidelity dimensions\.

##### Timestamp fidelity

Timestamp fidelity evaluates the generated time axis independently of feature values\. It checks temporal validity throughTemporal Order Consistency,TimestampUniqueness, andTemporal Range Compliance; sampling behavior throughRegularity ConsistencyandGrid Completenessfor regular series orTime Interval Distribution Similarityfor irregular series; and trajectory span throughTrajectory Duration Similarity\. These metrics are computed before post\-processing\. Full definitions are provided in Appendix[A\.2](https://arxiv.org/html/2607.15606#A1.SS2)\.

##### Cross\-sectional fidelity

Cross\-sectional fidelity evaluates whether feature distributions are preserved at aligned time points rather than only after pooling all records\. It applies when the dataset uses absolute time and contains dependent trajectories\. We partition the temporal domain into intervals and compute distributional similarity within each interval\. The instantiated metrics cover numerical marginals \(CS\-KSComplement\), categorical marginals \(CS\-TVComplement\), summary statistics, range and category coverage, and bivariate dependencies through correlation and contingency similarity\. Full definitions are provided in Appendix[A\.3](https://arxiv.org/html/2607.15606#A1.SS3)\.

##### Longitudinal fidelity

Longitudinal fidelity evaluates whether within\-entity dynamics are preserved over time\. Step\-level metrics compare local changes usingFirstDiffKSComplementfor numerical increments andTransMatrixTVDComplementfor categorical state transitions\. Trajectory\-level metrics compare longer\-range sequential structure usingAutoCorrSimilarity,MLD\-TS, andTT\-Wasserstein Distancewhere fixed\-length trajectories are available\. Full definitions are provided in Appendix[A\.4](https://arxiv.org/html/2607.15606#A1.SS4)\.

##### Structural fidelity

Structural fidelity evaluates whether the temporal relational structure of the data is preserved\.SequenceLengthSimilarityapplies to all schemas by comparing the distribution of trajectory lengths\. Multi\-child schemas addTemporalCardinalityShapeSimilarityandDynamic K\-Hop Correlation Similarityto test whether child\-record counts and cross\-table correlations evolve correctly over time\. Full definitions are provided in Appendix[A\.5](https://arxiv.org/html/2607.15606#A1.SS5)\.

### 3\.4\.Trajectory\-aware Utility and Privacy

##### Utility

Fidelity scores alone do not determine whether synthetic data supports downstream analysis\. Seq2Synth adopts the Machine Learning Efficiency protocol, training models on synthetic data and testing them on real data\. For sequential tabular data, we evaluate trajectory\-level utility withMLE\-TS\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)and additionally reportMLE\-Temporal, where historical context is included in the predictive input\. The protocol is provided in Appendix[A\.6](https://arxiv.org/html/2607.15606#A1.SS6)\.

##### Privacy

Standard row\-level privacy metrics such asDCRandNNDRignore whether a synthetic record matches a real record at the same time point or as part of the same trajectory\. Seq2Synth therefore adds cross\-sectionally restricted nearest\-neighbor metrics,CS\-DCRandCS\-NNDR, and annn\-gram privacy score,NGP​\(n\)=1−NgramExposure​\(n\)\\texttt\{NGP\}\(n\)=1\-\\texttt\{NgramExposure\}\(n\), where higher is safer\. Together these metrics distinguish incidental row\-level overlap from time\-aligned or sequential leakage\. Full definitions are provided in Appendix[A\.6](https://arxiv.org/html/2607.15606#A1.SS6)\.

## 4\.Experiments

### 4\.1\.Experimental Setup

We evaluate eight generative models on 13 sequential tabular datasets spanning six domains, whose temporal and structural characteristics are categorized in Table[2](https://arxiv.org/html/2607.15606#S4.T2)\. We use 7 datasets as the core set because each can be synthesized by at least six of the seven broadly applicable baselines, enabling fairer cross\-model comparison\. Crucially, these taxonomic axes dictate the applicability of our proposed evaluation dimensions \(as detailed in Table[9](https://arxiv.org/html/2607.15606#A0.T9)\)\. Detailed row\-level statistics and qualitative descriptions for each dataset are deferred to Online Appendix D\.3\. The evaluated models include: ClavaDDPM\(Panget al\.,[2024](https://arxiv.org/html/2607.15606#bib.bib7)\), RCTGAN\(Gueyeet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib11)\), RDBDiff\(Ketataet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib14)\), REaLTabFormer \(RTF\)\(Solatorio and Dupriez,[2023](https://arxiv.org/html/2607.15606#bib.bib9)\), RGCLD\(Hudovernik,[2024](https://arxiv.org/html/2607.15606#bib.bib12)\), RelDiff\(Hudoverniket al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib8)\), SDV\(Patkiet al\.,[2016](https://arxiv.org/html/2607.15606#bib.bib10)\), and TabDiT\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)\. All metric inputs follow the protocol in Section[3\.2](https://arxiv.org/html/2607.15606#S3.SS2):sdandtsare computed on raw generator outputs,csandstuse the default sparse variant, andlguses the interpolation\-fill variant when complete trajectories are required\. See Online Appendix D for implementation details\.

### 4\.2\.Results

Table 2\.Taxonomy and temporal\-structural characteristics of sequential tabular datasets\. Abs\./Rel\. denote absolute/relative time; Reg\./Irreg\. denote regular/irregular periodicity; Dep\./Indep\. denote dependent/independent trajectories\. M\-Child, M\-Parent, and M\-C&P denote multi\-child, multi\-parent, and multi\-child\-and\-parent schemas\. The first seven rows constitute the core set, selected because each dataset can be synthesized by at least six broadly applicable baselines\.A taxonomy table of thirteen sequential tabular datasets used in the benchmark\. Each row lists a dataset and characterizes it by domain, time representation, periodicity, trajectory independence, and data structure\. The first seven rows form the core evaluation set used for main cross\-model comparison\. The datasets span retail, healthcare, finance, industrial, transportation, and IT systems domains, and include both absolute and relative time representations, regular and irregular periodicity, dependent and independent trajectories, and linear, multi\-child, multi\-parent, and single\-table structures\.DatasetDomainTimeRep\.Period\.Traj\.Indep\.DataStruct\.RossmannRetailAbs\.Reg\.Dep\.LinearBerkaFinanceAbs\.Irreg\.Dep\.LinearFannie MaeFinanceAbs\.Reg\.Dep\.LinearWalmartRetailAbs\.Reg\.Dep\.M\-ChildAirBnBRetailRel\.Irreg\.Dep\.LinearPTB\-XLHealthRel\.Reg\.Indep\.LinearFreddie MacFinanceAbs\.Reg\.Dep\.LinearCiti BikeTransportAbs\.Irreg\.Dep\.SingleCMAPSSIndustryRel\.Reg\.Indep\.SingleCouponRetailAbs\.Irreg\.Dep\.M\-C&PGoogle ClusterITRel\.BothIndep\.M\-ChildH&MRetailAbs\.Irreg\.Dep\.M\-ParentHome CreditFinanceRel\.Reg\.Dep\.M\-ChildWe organize the results around three empirical findings that follow the benchmark design in Section[3\.2](https://arxiv.org/html/2607.15606#S3.SS2)\. First, static\-distribution evaluation is not a reliable proxy for temporal fidelity: model rankings change substantially when timestamp, longitudinal, and structural fidelity are measured directly\. Second, the resulting failures are architecture\-coherent rather than random: autoregressive models tend to preserve within\-trajectory order but struggle with relational cardinality, while joint and relational generators better preserve some schema\-level structure but often fail on timestamp validity and trajectory dynamics\. Third, temporal evaluation changes how we interpret both privacy and downstream utility\. Online Appendix E reports complete sub\-metric tables for the seven core datasets; the main text uses Rossmann and Walmart as representative deep dives because they expose the full timestamp/trajectory and multi\-child structural failure modes, respectively\.

Table 3\.Per\-dataset fidelity scores on the seven core datasets across five evaluation dimensions\. Higher is better; “–” denotes inapplicable cases\. Bold and underline indicate the best and second\-best scores per dataset–metric row\.DatasetMetricClavaDDPMRCTGANRDBDiffRTFRGCLDRelDiffSDVTabDiTRossmannsd0\.8500\.8100\.858¯\\underline\{0\.858\}0\.8090\.8210\.7990\.7340\.932\\mathbf\{0\.932\}ts0\.6070\.5620\.6080\.823¯\\underline\{0\.823\}0\.5980\.6020\.5650\.824\\mathbf\{0\.824\}cs0\.912¯\\underline\{0\.912\}0\.8080\.912¯\\underline\{0\.912\}0\.8820\.8970\.8170\.6350\.965\\mathbf\{0\.965\}lg0\.9170\.8720\.9150\.948¯\\underline\{0\.948\}0\.9020\.8820\.7890\.975\\mathbf\{0\.975\}st1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}Berkasd0\.9480\.8650\.992\\mathbf\{0\.992\}0\.951¯\\underline\{0\.951\}0\.9220\.8980\.6950\.909ts0\.5940\.6200\.7590\.907\\mathbf\{0\.907\}0\.7310\.6030\.5350\.777¯\\underline\{0\.777\}cs0\.691¯\\underline\{0\.691\}0\.6320\.829\\mathbf\{0\.829\}0\.6650\.6710\.6260\.4480\.651lg0\.8770\.8580\.949\\mathbf\{0\.949\}0\.896¯\\underline\{0\.896\}0\.8850\.8680\.6860\.890st0\.9930\.9521\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9930\.9520\.8140\.958Fannie Maesd0\.900¯\\underline\{0\.900\}0\.8600\.8760\.8540\.906\\mathbf\{0\.906\}0\.8990\.814–ts0\.5670\.5500\.571¯\\underline\{0\.571\}0\.4740\.5030\.598\\mathbf\{0\.598\}0\.481–cs0\.965\\mathbf\{0\.965\}0\.8520\.8700\.7770\.876¯\\underline\{0\.876\}0\.8490\.772–lg0\.8200\.7870\.7810\.8040\.858¯\\underline\{0\.858\}0\.8220\.864\\mathbf\{0\.864\}–st0\.998\\mathbf\{0\.998\}0\.9530\.8220\.8170\.990¯\\underline\{0\.990\}0\.7500\.848–Walmartsd0\.7960\.8610\.8150\.7190\.950\\mathbf\{0\.950\}0\.898¯\\underline\{0\.898\}0\.857–ts0\.610\\mathbf\{0\.610\}0\.5260\.608¯\\underline\{0\.608\}0\.4550\.6000\.5980\.522–cs0\.8670\.7850\.896\\mathbf\{0\.896\}0\.6050\.891¯\\underline\{0\.891\}0\.8280\.746–lg0\.887\\mathbf\{0\.887\}0\.8440\.8680\.6900\.872¯\\underline\{0\.872\}0\.8520\.814–st0\.8640\.7310\.887\\mathbf\{0\.887\}0\.5180\.882¯\\underline\{0\.882\}0\.8040\.786–Airbnbsd0\.967\\mathbf\{0\.967\}0\.9090\.963¯\\underline\{0\.963\}0\.8790\.9250\.9370\.7110\.923ts0\.875\\mathbf\{0\.875\}0\.8400\.8240\.7770\.8430\.860¯\\underline\{0\.860\}0\.8110\.860¯\\underline\{0\.860\}cs––––––––lg0\.9640\.970\\mathbf\{0\.970\}0\.9650\.9670\.969¯\\underline\{0\.969\}0\.969¯\\underline\{0\.969\}0\.9090\.965st0\.9870\.9241\.000\\mathbf\{1\.000\}0\.6310\.9811\.000\\mathbf\{1\.000\}0\.9380\.912PTB\-XLsd0\.886¯\\underline\{0\.886\}0\.5760\.896\\mathbf\{0\.896\}0\.6250\.6920\.6690\.758–ts0\.5940\.3300\.5771\.000\\mathbf\{1\.000\}0\.5340\.5910\.675¯\\underline\{0\.675\}–cs––––––––lg0\.927\\mathbf\{0\.927\}0\.8410\.9090\.9150\.9060\.922¯\\underline\{0\.922\}0\.920–st1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9990\.9991\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}–Freddie Macsd0\.9440\.8820\.986\\mathbf\{0\.986\}0\.8530\.975¯\\underline\{0\.975\}0\.9200\.810–ts0\.7130\.6880\.6600\.5810\.7360\.752\\mathbf\{0\.752\}0\.747¯\\underline\{0\.747\}–cs0\.9240\.8430\.982\\mathbf\{0\.982\}0\.7770\.930¯\\underline\{0\.930\}0\.8470\.740–lg0\.8420\.7970\.915\\mathbf\{0\.915\}0\.7840\.875¯\\underline\{0\.875\}0\.8410\.780–st0\.9950\.9721\.000\\mathbf\{1\.000\}0\.6950\.9931\.000\\mathbf\{1\.000\}0\.965–##### Finding 1: Static\-distribution rankings do not summarize temporal fidelity\.

Table[3](https://arxiv.org/html/2607.15606#S4.T3)reports per\-dataset fidelity scores across seven core datasets under five evaluation dimensions: the static\-distribution baseline \(sd\) used in prior benchmarks\(Qianet al\.,[2023](https://arxiv.org/html/2607.15606#bib.bib24); Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\), timestamp validity \(ts\), cross\-sectional distributional evolution \(cs\), longitudinal trajectory dynamics \(lg\), and structural consistency \(st\)\. The results show that fidelity is strongly dimension\-dependent: models with highsdscores do not consistently dominate the temporal\-aware dimensions, and the best\-performing model often changes acrossts,lg, andst\. Based on this observation, we analyze rank disagreement between static\-distribution and temporal\-aware evaluation\.

Table 4\.Rank disagreement betweensdand temporal dimensions\. Spearmanρ\\rhoand inversion rates are computed across models within each dataset; pooledρ\\rhoconcatenates within\-dataset ranks\. “–” denotes inapplicable\.A table reporting rank disagreement between static\-distribution evaluation and temporal\-aware fidelity dimensions\. For each dataset, the table compares static\-distribution rankings against timestamp, cross\-sectional, longitudinal, and structural rankings using Spearman correlation and the fraction of inverted model pairs\. Lower or negative correlations and higher inversion fractions indicate stronger disagreement between static and temporal\-aware evaluations\. The table shows that static\-distribution rankings often disagree with temporal\-aware rankings, especially for timestamp and longitudinal dimensions, supporting the need for separate temporal fidelity evaluation\.Datasetsdvstssdvscssdvslgsdvsstρ\\rhoInv\.ρ\\rhoInv\.ρ\\rhoInv\.ρ\\rhoInv\.Airbnb0\.7140\.7140\.210\.21––−0\.071\-0\.0710\.570\.570\.7550\.7550\.220\.22Berka0\.5950\.5950\.290\.290\.9050\.9050\.110\.110\.9050\.9050\.110\.110\.4970\.4970\.280\.28Fannie Mae0\.5000\.5000\.330\.330\.8570\.8570\.140\.140\.0710\.0710\.480\.480\.4290\.4290\.380\.38Freddie Mac−0\.107\-0\.1070\.520\.521\.0001\.0000\.000\.001\.0001\.0000\.000\.000\.7750\.7750\.200\.20PTB\-XL0\.1430\.1430\.480\.48––0\.3930\.3930\.330\.330\.4080\.4080\.170\.17Rossmann0\.5710\.5710\.250\.250\.9290\.9290\.070\.070\.6900\.6900\.210\.21––Walmart0\.1070\.1070\.430\.430\.3210\.3210\.330\.330\.2500\.2500\.380\.380\.2860\.2860\.380\.38Mean \(per\-ds\)0\.3600\.3600\.360\.360\.8020\.8020\.130\.130\.4630\.4630\.300\.300\.5250\.5250\.270\.27Pooled0\.4030\.403–0\.8190\.819–0\.4770\.477–0\.4970\.497–Table[4](https://arxiv.org/html/2607.15606#S4.T4)shows thatsd\-based evaluation is a poor proxy for temporal fidelity\. Across the seven core datasets, the rankings induced by timestamp, longitudinal, and structural fidelity diverge substantially from thesd\-based ranking, with mean Spearman correlations of0\.360\.36,0\.460\.46, and0\.530\.53, respectively\. The corresponding inversion rates are also high:36%36\\%,30%30\\%, and27%27\\%of model pairs reverse their ordering relative tosd\. Thus, models that appear competitive under static\-distribution evaluation may fail to preserve temporal validity, trajectory dynamics, or structural consistency\.

Cross\-sectional fidelity is the only temporal\-aware dimension that remains closely aligned withsdevaluation, with pooledρ=0\.82\\rho=0\.82and a mean inversion rate of13%13\\%\. This is because the cross\-sectional dimension evaluates distributional similarity within individual time slices and then aggregates the slice\-wise scores over time\. As a result, it retains much of the ranking signal captured by static\-distribution evaluation, but with a finer temporal resolution\. This suggests that cross\-sectional fidelity contributes less by producing a different global model ranking and more by diagnosing whether distributional fidelity is stable across time\. A model can achieve a strong pooledsdscore while still failing on specific time slices, and the cross\-sectional dimension is designed to expose such temporally localized distributional failures\. These rank disagreements establish the main empirical premise of Seq2Synth: temporal fidelity cannot be reduced to a single architecture\-independent notion of quality\. The next analysis explains why the rankings diverge by decomposing model behavior into timestamp, cross\-sectional, longitudinal, and structural failure modes\.

##### Finding 2: Temporal sub\-metrics expose model\-specific failures\.

Table 5\.Timestamp sub\-metric scores on Rossmann before post\-processing\. All scores lie in\[0,1\]\[0,1\], with higher values indicating better timestamp fidelity\. Bold and underline mark the best and second\-best scores per column\.A results table reporting timestamp sub\-metric scores on the Rossmann dataset before post\-processing\. Rows compare synthetic data generation models, and columns report timestamp order consistency, timestamp uniqueness, duration similarity, regularity consistency, and grid completeness\. Scores range from zero to one, with higher values indicating better timestamp fidelity\.ModelOrderUniqueDurationRegularityGridClavaDDPM0\.5070\.5070\.6290\.6290\.4620\.4620\.4020\.4020\.6440\.644RCTGAN0\.512\\mathbf\{0\.512\}0\.5940\.5940\.2870\.2870\.3720\.3720\.6110\.611RDBDiff0\.510¯\\underline\{0\.510\}0\.6280\.6280\.4660\.4660\.4020\.4020\.6440\.644RTF0\.0010\.0010\.999\\mathbf\{0\.999\}0\.942¯\\underline\{0\.942\}0\.997\\mathbf\{0\.997\}0\.999\\mathbf\{0\.999\}RGCLD0\.5070\.5070\.6190\.6190\.4350\.4350\.3920\.3920\.6360\.636RelDiff0\.5090\.5090\.6160\.6160\.5070\.5070\.3690\.3690\.6180\.618SDV0\.5080\.5080\.5940\.5940\.3500\.3500\.3640\.3640\.5960\.596TabDiT0\.0230\.0230\.978¯\\underline\{0\.978\}1\.000\\mathbf\{1\.000\}0\.959¯\\underline\{0\.959\}0\.983¯\\underline\{0\.983\}Timestamp\.Timestamps encode trajectory\-level structure that ordinary marginal fidelity metrics cannot capture\. We first examine whether the eight models generate valid timestamp structure on Rossmann, including uniqueness, regular spacing, grid coverage, and trajectory duration\. Table[5](https://arxiv.org/html/2607.15606#S4.T5)reports timestamp sub\-metric scores on Rossmann, a regular time\-series dataset\. The columns denoteTemporalOrderConsistency,TimestampUniqueness,TrajectoryDurationSimilarity,RegularityConsistency, andGridCompleteness, respectively, all computed before post\-processing\. Together, these metrics distinguish misordered records, duplicate timestamps, unrealistic durations, irregular intervals, and incomplete observation grids\. The results reveal a clear architectural divide\. For the timestamp properties that remain meaningful after user\-side reordering—uniqueness, duration, regularity, and grid coverage—RTF and TabDiT occupy the top two ranks with scores above0\.940\.94, while the six joint\-generation models remain substantially lower\. This gap reflects the advantage of autoregressive decoding: by emitting events sequentially and conditioning each timestamp on previously generated ones, RTF and TabDiT better preserve uniqueness, regular spacing, duration, and grid coverage\. In contrast, joint\-generation models sample timestamps in parallel with other features, leading to duplicate timestamps, mismatched durations, irregular intervals, and missing grid slots\. These errors are invisible tosdand cannot be resolved by simple reordering\.

Table 6\.Cross\-sectional sub\-metric profiles on Rossmann by sparse \(NaN\-fill\) variant\. All scores are computed per time slice and lie in\[0,1\]\[0,1\], with higher values indicating better cross\-sectional fidelity\. Bold and underline mark the best and second\-best scores per column\.A results table reporting cross\-sectional sub\-metric scores on the Rossmann dataset under the sparse not\-a\-number fill variant\. Rows compare synthetic data generation models, and columns report numerical marginal similarity, categorical marginal similarity, summary\-statistic similarity, category coverage, and contingency similarity\. Scores range from zero to one, with higher values indicating better cross\-sectional fidelity\.ModelCS\-KSCompCS\-TVCompCS\-StatSimCS\-CatCovCS\-ContSimClavaDDPM0\.951¯\\underline\{0\.951\}0\.9120\.9120\.7750\.7750\.969¯\\underline\{0\.969\}0\.8280\.828RCTGAN0\.8740\.8740\.6880\.6880\.7230\.7230\.972\\mathbf\{0\.972\}0\.5050\.505RDBDiff0\.9480\.9480\.913¯\\underline\{0\.913\}0\.7740\.7740\.969¯\\underline\{0\.969\}0\.830¯\\underline\{0\.830\}RTF0\.9040\.9040\.8280\.8280\.875¯\\underline\{0\.875\}0\.9100\.9100\.7020\.702RGCLD0\.9400\.9400\.8920\.8920\.7650\.7650\.9350\.9350\.8060\.806RelDiff0\.8810\.8810\.7380\.7380\.6810\.6810\.972\\mathbf\{0\.972\}0\.5630\.563SDV0\.5620\.5620\.4960\.4960\.7270\.7270\.7340\.7340\.2630\.263TabDiT0\.996\\mathbf\{0\.996\}0\.947\\mathbf\{0\.947\}0\.947\\mathbf\{0\.947\}0\.972\\mathbf\{0\.972\}0\.896\\mathbf\{0\.896\}Cross\-sectional dimension\.Table[6](https://arxiv.org/html/2607.15606#S4.T6)shows the cross\-sectional sub\-metric profiles on Rossmann\. The displayed columns correspond toCS\-KSComplement,CS\-TVComplement,CS\-StatisticSimilarity,CS\-CategoryCoverage, andCS\-ContingencySimilarity\. TabDiT has the strongest cross\-sectional profile, ranking best on most sub\-metrics\. Some models show asymmetric behavior that an aggregate score can obscure: RCTGAN and RelDiff achieve high category coverage but much lower contingency similarity, indicating that they recover per\-slice category values without preserving their joint combinations\. SDV shows the weakest profile, especially on contingency similarity\. These results suggest that cross\-sectional fidelity requires more than matching marginal distributions or category coverage within each time slice; it also requires preserving relationships among features\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x3.png)A heatmap showing longitudinal fidelity sub\-metric profiles on the Rossmann dataset under the interpolation\-fill variant\. Rows correspond to synthetic data generation models, and columns correspond to three longitudinal sub\-metrics: first\-difference KS\-complement, transition\-matrix TV\-complement, and autocorrelation similarity\. Cell values range from zero to one, with darker red colors indicating higher scores and darker blue colors indicating lower scores\. The heatmap shows that TabDiT achieves the highest scores on first\-difference and transition\-matrix metrics, while ClavaDDPM achieves the highest autocorrelation similarity\.

Figure 3\.Longitudinal sub\-metric profiles on Rossmann under the interpolation\-fill variant\. All scores lie in\[0,1\]\[0,1\], with higher values indicating better longitudinal fidelity\.Longitudinal dimension\.Figure[3](https://arxiv.org/html/2607.15606#S4.F3)reports the longitudinal sub\-metric profiles on Rossmann\. The columns correspond toFirstDiffKSComplement,TransMatrixTVDComplement, andAutoCorrSimilarity\. TabDiT exhibits the strongest longitudinal profile, leading on the first\-difference and transition\-matrix metrics, while RTF also performs strongly on the order\-sensitive metrics\. This pattern is consistent with the within\-trajectory advantage of autoregressive decoding observed in the timestamp analysis\. The differences across sub\-metrics show that longitudinal fidelity is not a single property\. ClavaDDPM and SDV preserve autocorrelation relatively well, but are weaker on local changes and transition patterns, while RTF shows the opposite behavior\. Thus, local changes, transitions, and temporal dependence should be evaluated separately because they capture different aspects of within\-entity dynamics\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x4.png)A grouped bar chart showing structural fidelity sub\-metric scores on the Walmart dataset\. The x\-axis lists synthetic data generation models, and the y\-axis reports normalized scores from zero to one, with higher values indicating better structural fidelity\. For each model, three bars represent sequence\-length similarity, temporal\-cardinality similarity, and dynamic\-hop similarity\. The chart shows that RDBDiff, RGCLD, ClavaDDPM, RelDiff, and SDV achieve relatively high sequence\-length and dynamic\-hop scores, while temporal\-cardinality scores are generally lower across models\. RTF has the lowest sequence\-length and temporal\-cardinality scores but maintains a moderate dynamic\-hop score\.

Figure 4\.Structural fidelity sub\-metrics on Walmart\. All scores are normalized in\[0,1\]\[0,1\], with higher values indicating better structural fidelity\.Temporal relational structure\.Figure[4](https://arxiv.org/html/2607.15606#S4.F4)describes structural sub\-metric profiles on Walmart, the only core dataset with applicablestsub\-metric data\. The 3 sub\-metrics evaluateSequence Length Similarity,Temporal Cardinality Shape Similarity, andDynamic K\-Hop Correlation Similarity\. The first 2 sub\-metrics are computed from raw generator output, whereasDynamicK\-HopCorrelationSimilarityuses the sparse variant\. RTF reveals a limitation of autoregressive sequence generation in relational settings\. Although it performs strongly on timestamp and longitudinal dimensions, its low structural fidelity is mainly driven by failures inSequenceLengthSimilarityandTemporalCardinalityShapeSimilarity, indicating that it does not reliably control the number of child records per parent or their temporal cardinality patterns\. By contrast, relational diffusion models such as RDBDiff and ClavaDDPM improve substantially underst, despite weakersdrankings, because their joint generation under the relational schema better preserves sequence length and cross\-table correlation structure across parent entities\.

##### Finding 3: Temporal evaluation provides a complementary lens beyond static privacy and utility metrics\.

Table 7\.Privacy metric profiles on Rossmann\.DCRandCS\-DCRreport raw median nearest\-neighbor distances\.NNDR,CS\-NNDR, andNGP\(n\) forn∈\{1,3\}n\\in\\\{1,3\\\}are normalized scores in\[0,1\]\[0,1\], whereNGP\(n\)=1−NgramExposure​\(n\)=1\-\\texttt\{NgramExposure\}\(n\)\. Higher values are safer; bold/underline indicate best/second\-best\.A results table reporting privacy metric profiles on the Rossmann dataset\. Rows compare synthetic data generation models, and columns are grouped into row\-level privacy, cross\-sectional privacy, and n\-gram privacy\. Higher values indicate safer behavior and lower privacy risk\.ModelRow\-levelCross\-sectionalnn\-gram PrivacyDCRNNDRCS\-DCRCS\-NNDRNGP\(1\)NGP\(3\)ClavaDDPM8\.068\.060\.7070\.70749\.4649\.460\.6530\.6530\.0020\.0020\.9120\.912RCTGAN9\.229\.220\.7090\.70973\.4873\.480\.6950\.6950\.0740\.0740\.998¯\\underline\{0\.998\}RDBDiff6\.086\.080\.6620\.66216\.2416\.240\.4890\.4890\.0000\.0000\.8330\.833RTF9\.069\.060\.721¯\\underline\{0\.721\}64\.8064\.800\.742¯\\underline\{0\.742\}0\.0280\.0280\.1800\.180RGCLD8\.068\.060\.7070\.70754\.7254\.720\.6970\.6970\.0140\.0140\.9070\.907RelDiff12\.04\\mathbf\{12\.04\}0\.7030\.70396\.72\\mathbf\{96\.72\}0\.6930\.6930\.209¯\\underline\{0\.209\}0\.998¯\\underline\{0\.998\}SDV9\.85¯\\underline\{9\.85\}0\.7070\.70786\.76¯\\underline\{86\.76\}0\.6610\.6610\.221\\mathbf\{0\.221\}0\.999\\mathbf\{0\.999\}TabDiT11\.0011\.000\.766\\mathbf\{0\.766\}62\.8462\.840\.753\\mathbf\{0\.753\}0\.0080\.0080\.2670\.267Privacy\.StandardDCR,NNDR, and single\-row exposure treat synthetic and real records as exchangeable across time\. Two practical concerns motivate temporal restrictions\. First, two records sharing values at*unrelated*timestamps are often not a re\-identification risk: bounded row vocabularies make such incidental overlap common \(for instance, 20% of session records in Airbnb share identical row\-level values with at least one other record\), and the concern is whether identifying values concentrate at the*same*time slice as a real record\. Second, plausible synthetic rows can still reproduce*consecutive sub\-sequences*of a real trajectory, which row\-level overlap counts cannot detect\. We therefore compare row\-level metrics withCS\-DCR,CS\-NNDR, andnn\-gram privacy \(NGP​\(n\)=1−NgramExposure​\(n\)\\texttt\{NGP\}\(n\)=1\-\\texttt\{NgramExposure\}\(n\)\) on Rossmann\.

Under the*higher is safer*convention, Table[7](https://arxiv.org/html/2607.15606#S4.T7)shows that row\-level privacy metrics can misrepresent temporal privacy risk\.

Table 8\.Correlation results for MLE\-TS and MLE\-Temporal\. Bold/underline mark best/second\-best per row\.Correlation results on the four datasets shared by MLE\-TS and MLE\-Temporal\. The table reports correlations between downstream utility and three fidelity scores under both evaluation protocols\. The Average row denotes the mean correlation across the four datasets\. Bold and underlined values indicate the best and second\-best correlations within each row, respectively\.DatasetMLE\-TSMLE\-TemporalρSD\\rho\_\{\\mathrm\{SD\}\}ρlong\\rho\_\{\\mathrm\{long\}\}ρall\\rho\_\{\\mathrm\{all\}\}ρSD\\rho\_\{\\mathrm\{SD\}\}ρlong\\rho\_\{\\mathrm\{long\}\}ρall\\rho\_\{\\mathrm\{all\}\}Rossmann0\.6900\.5240\.6670\.9290\.6900\.786Fannie Mae0\.3210\.3210\.107−0\.143\-0\.1430\.643−0\.214\-0\.214Walmart−0\.464\-0\.4640\.6070\.5000\.0710\.6430\.750Freddie Mac0\.1430\.1430\.2140\.7500\.7500\.821Average0\.1730\.3990\.3720\.4020\.6820\.536

Time\-agnostic nearest\-neighbor metrics such asDCRandNNDRignore whether matched synthetic and real rows belong to the same time slice\. In low\-cardinality sequential data, this can count incidental cross\-time matches as privacy risk; the largerCS\-DCRvalues indicate that row\-level nearest neighbors come from unrelated timestamps\. Conversely, single\-row exposure can miss sequential leakage:NGP\(1\)does not detect copied consecutive sub\-sequences\. RTF and TabDiT illustrate this failure, appearing safe under row\-level metrics but becoming the riskiest models underNGP\(3\)\. Thus, the autoregressive mechanism that improves within\-trajectory fidelity can increase trajectory\-level privacy risk\. Results on the remaining 6 datasets are reported in Online Appendix E\.5\.

Utility\.Table[8](https://arxiv.org/html/2607.15606#S4.T8)reports correlation results on the four datasets shared byMLE\-TSandMLE\-Temporal\. The results show thatsd\-based evaluation does not fully explain downstream temporal utility\. UnderMLE\-TS, the average longitudinal correlation \(ρlong=0\.399\\rho\_\{\\mathrm\{long\}\}=0\.399\) is higher than thesdcorrelation \(ρSD=0\.173\\rho\_\{\\mathrm\{SD\}\}=0\.173\)\. The pattern becomes stronger underMLE\-Temporal, where longitudinal fidelity is more aligned with utility thansd\(ρlong=0\.682\\rho\_\{\\mathrm\{long\}\}=0\.682vs\.ρSD=0\.402\\rho\_\{\\mathrm\{SD\}\}=0\.402\)\. This increase suggests that when the downstream protocol explicitly preserves chronological structure, utility depends more on whether synthetic data captures within\-trajectory dynamics than on whether it matches static marginal distributions alone\. This gap widens fromMLE\-TStoMLE\-Temporal, suggesting that temporal fidelity becomes increasingly task\-relevant as the downstream protocol uses more historical context\. Full results are available in Online Appendices E\.2 and E\.3\.

## 5\.Discussion

##### Implications for benchmark use\.

The results provide empirical evidence that Seq2Synth should be used as a diagnostic protocol rather than as a single leaderboard score\. Static\-distribution fidelity remains useful for checking pooled record\-level plausibility, but it is insufficient for model selection when the deployment depends on temporal behavior\. The taxonomy\-to\-metric mapping is therefore essential: timestamp and longitudinal metrics test whether individual trajectories are valid, cross\-sectional metrics test whether population structure evolves correctly over absolute time, and structural metrics test whether relational cardinalities and cross\-table dependencies are preserved\. These dimensions should be interpreted jointly, because a model can be strong along one temporal axis and fail along another\. The same principle applies to privacy and utility: row\-level privacy and static downstream performance should be complemented by trajectory\-aware views when sequential leakage or temporal prediction is the relevant risk\.

##### Implications for generator design\.

The failure modes identified by Seq2Synth point to three concrete design requirements for future sequential\-tabular generators\. First, timestamps should be modeled as ordered objects rather than as ordinary continuous attributes; otherwise, a model can match timestamp marginals while producing invalid chronological structure\. Second, autoregressive generators need explicit absolute\-time anchoring, such as calendar embeddings, anchor tokens, or auxiliary timestamp losses, so that token position is not confused with calendar time\. Third, sequence length and relational cardinality should be conditioned on directly rather than left to emerge implicitly, especially in multi\-table schemas where parent–child counts evolve over time\. These changes do not require a new model family: they can be incorporated into existing diffusion, autoregressive, or relational generators through constrained decoding, auxiliary objectives, or conditioning inputs\.

## 6\.Conclusion

We presentedSeq2Synth, a taxonomy\-guided benchmark for evaluating synthetic sequential tabular data\. Rather than treating all datasets with a fixed metric suite, Seq2Synth maps time representation, sampling regularity, trajectory dependence, and schema structure to applicable temporal fidelity dimensions: timestamp, cross\-sectional, longitudinal, and structural fidelity\. Across a 13\-dataset benchmark and eight generators, our experiments show that static\-distribution fidelity is not a reliable proxy for temporal fidelity: models that appear strong under conventional evaluation can still produce invalid timestamps, distorted trajectories, or inconsistent temporal relational structure\. The trajectory\-aware utility and privacy analyses further show that temporal evaluation changes how model quality and leakage risk should be interpreted\. These findings support a simple principle: synthetic sequential tabular data should be evaluated as temporally ordered trajectories and relational processes, not as pooled rows\.

## References

- S\. A\. Assefa, D\. Dervovic, M\. Mahfouz, R\. E\. Tillman, P\. Reddy, and M\. Veloso \(2020\)Generating synthetic data in finance: opportunities, challenges and pitfalls\.InProceedings of the first ACM international conference on AI in finance,pp\. 1–8\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1)\.
- T\. Chen and C\. Guestrin \(2016\)Xgboost: a scalable tree boosting system\.InProceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining,pp\. 785–794\.Cited by:[§D\.6](https://arxiv.org/html/2607.15606#A4.SS6.p1.1)\.
- Citi Bike NYC \(2013\)Citi bike trip history data\.Note:Accessed via KaggleExternal Links:[Link](https://www.kaggle.com/datasets/sujan97/citibike-system-data)Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p10.1)\.
- DataCebo, Inc\. \(2020\)SDMetrics: the synthetic data metrics library\.GitHub\.Note:[https://github\.com/sdv\-dev/SDMetrics](https://github.com/sdv-dev/SDMetrics)Cited by:[§A\.5](https://arxiv.org/html/2607.15606#A1.SS5.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.6.2.1.2.1)\.
- Y\. Du and N\. Li \(2025\)Systematic assessment of tabular data synthesis\.InProceedings of the 2025 ACM SIGSAC Conference on Computer and Communications Security,pp\. 2414–2428\.Cited by:[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.3.2.1.3.1)\.
- Fannie Mae \(2026\)Single\-Family Loan Performance Data\.Note:[https://capitalmarkets\.fanniemae\.com/credit\-risk\-transfer/single\-family\-credit\-risk\-transfer/fannie\-mae\-single\-family\-loan\-performance\-data](https://capitalmarkets.fanniemae.com/credit-risk-transfer/single-family-credit-risk-transfer/fannie-mae-single-family-loan-performance-data)Updated January 30, 2026Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p6.1)\.
- Freddie Mac \(2026\)Single\-Family Loan\-Level Dataset\.Note:[https://www\.freddiemac\.com/research/datasets/sf\-loanlevel\-dataset](https://www.freddiemac.com/research/datasets/sf-loanlevel-dataset)Release 46Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p6.1)\.
- F\. Garuti, E\. Sangineto, S\. Luetto, L\. Forni, and R\. Cucchiara \(2025\)Diffusion transformers for tabular data time series generation\.External Links:2504\.07566,[Link](https://arxiv.org/abs/2504.07566)Cited by:[Table 9](https://arxiv.org/html/2607.15606#A0.T9.28.28.28.2.1),[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p11.1),[§D\.5](https://arxiv.org/html/2607.15606#A4.SS5.SSS0.Px1.p1.1),[§1](https://arxiv.org/html/2607.15606#S1.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[§3\.4](https://arxiv.org/html/2607.15606#S3.SS4.SSS0.Px1.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.8.2.1.3.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- M\. Gueye, Y\. Attabi, and M\. Dumas \(2023\)Row conditional\-tgan for generating synthetic relational databases\.InICASSP 2023 \- 2023 IEEE International Conference on Acoustics, Speech and Signal Processing \(ICASSP\),Vol\.,pp\. 1–5\.External Links:[Document](https://dx.doi.org/10.1109/ICASSP49357.2023.10096001)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- H&M Group \(2021\)H&M personalized fashion recommendations\.Note:[https://www\.kaggle\.com/competitions/h\-and\-m\-personalized\-fashion\-recommendations](https://www.kaggle.com/competitions/h-and-m-personalized-fashion-recommendations)Kaggle datasetCited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p3.1)\.
- haisland0909, S\. KATO, suharay, and W\. Cukierski \(2015\)Coupon purchase prediction\.Note:[https://kaggle\.com/competitions/coupon\-purchase\-prediction](https://kaggle.com/competitions/coupon-purchase-prediction)KaggleCited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p4.1)\.
- Home Credit Group \(2018\)Home credit default risk dataset\.External Links:[Link](https://www.kaggle.com/competitions/home-credit-default-risk)Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p7.1)\.
- V\. Hudovernik, M\. Xu, J\. Shi, L\. Šubelj, S\. Ermon, E\. Štrumbelj, and J\. Leskovec \(2025\)RelDiff: relational data generative modeling with graph\-based diffusion models\.External Links:2506\.00710,[Link](https://arxiv.org/abs/2506.00710)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- V\. Hudovernik \(2024\)Relational data generation with graph neural networks and latent diffusion models\.InNeurIPS 2024 Third Table Representation Learning Workshop,External Links:[Link](https://openreview.net/forum?id=MNLR2NYN2Z)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- M\. Jurkovic, V\. Hudovernik, and E\. Štrumbelj \(2025\)SyntheRela: a benchmark for synthetic relational database generation\.InWill Synthetic Data Finally Solve the Data Access Problem?,External Links:[Link](https://openreview.net/forum?id=ZfQofWYn6n)Cited by:[§A\.5](https://arxiv.org/html/2607.15606#A1.SS5.p3.2),[§A\.5](https://arxiv.org/html/2607.15606#A1.SS5.p4.2),[§D\.1](https://arxiv.org/html/2607.15606#A4.SS1.p1.1),[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p2.1),[§D\.5](https://arxiv.org/html/2607.15606#A4.SS5.SSS0.Px1.p1.1),[§1](https://arxiv.org/html/2607.15606#S1.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.5.2.1.3.1),[§4\.2](https://arxiv.org/html/2607.15606#S4.SS2.SSS0.Px1.p1.1)\.
- M\. A\. Ketata, D\. Lüdke, L\. Schwinn, and S\. Günnemann \(2025\)Joint relational database generation via graph\-conditional diffusion models\.arXiv preprint arXiv:2505\.16527\.External Links:[Link](https://arxiv.org/abs/2505.16527)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- A\. D\. Lautrup, T\. Hyrup, A\. Zimek, and P\. Schneider\-Kamp \(2024\)Syntheval: a framework for detailed utility and privacy evaluation of tabular synthetic data\.Data Mining and Knowledge Discovery39\(1\)\.External Links:ISSN 1573\-756X,[Link](http://dx.doi.org/10.1007/s10618-024-01081-4),[Document](https://dx.doi.org/10.1007/s10618-024-01081-4)Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.2.2.1.3.1)\.
- Z\. Li, X\. Lin, Z\. Liu, J\. Zou, Z\. Wu, L\. Zheng, D\. Fu, Y\. Zhu, H\. Hamann, H\. Tong, and J\. He \(2026\)Language in the flow of time: time\-series\-paired texts weaved into a unified temporal narrative\.InThe Fourteenth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=a1zBg9cBvt)Cited by:[Table 9](https://arxiv.org/html/2607.15606#A0.T9.27.27.27.2.1)\.
- E\. Ntoutsi, P\. Fafalios, U\. Gadiraju, V\. Iosifidis, W\. Nejdl, M\. Vidal, S\. Ruggieri, F\. Turini, S\. Papadopoulos, E\. Krasanakis,et al\.\(2020\)Bias in data\-driven artificial intelligence systems—an introductory survey\.Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery10\(3\),pp\. e1356\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1)\.
- W\. Pang, M\. Shafieinejad, L\. Liu, S\. Hazlewood, and X\. He \(2024\)ClavaDDPM: multi\-relational data synthesis with cluster\-guided diffusion models\.InProceedings of the 38th International Conference on Neural Information Processing Systems,NIPS ’24,Red Hook, NY, USA\.External Links:ISBN 9798331314385Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p3.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- N\. Patki, R\. Wedge, and K\. Veeramachaneni \(2016\)The synthetic data vault\.In2016 IEEE International Conference on Data Science and Advanced Analytics \(DSAA\),Vol\.,pp\. 399–410\.External Links:[Document](https://dx.doi.org/10.1109/DSAA.2016.49)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- V\. K\. Potluru, D\. Borrajo, A\. Coletta, N\. Dalmasso, Y\. El\-Laham, E\. Fons, M\. Ghassemi, S\. Gopalakrishnan, V\. Gosai, E\. Kreačić,et al\.\(2023\)Synthetic data applications in finance\.arXiv preprint arXiv:2401\.00081\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1)\.
- Z\. Qian, R\. Davis, and M\. van der Schaar \(2023\)Synthcity: a benchmark framework for diverse use cases of tabular synthetic data\.InAdvances in Neural Information Processing Systems,A\. Oh, T\. Naumann, A\. Globerson, K\. Saenko, M\. Hardt, and S\. Levine \(Eds\.\),Vol\.36,pp\. 3173–3188\.External Links:[Link](https://proceedings.neurips.cc/paper_files/paper/2023/file/09723c9f291f6056fd1885081859c186-Paper-Datasets_and_Benchmarks.pdf)Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.1.2.1.3.1),[§4\.2](https://arxiv.org/html/2607.15606#S4.SS2.SSS0.Px1.p1.1)\.
- P\. Rajpurkar, E\. Chen, O\. Banerjee, and E\. J\. Topol \(2022\)AI in health and medicine\.Nature medicine28\(1\),pp\. 31–38\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1)\.
- D\. Rankin, M\. Black, R\. Bond, J\. Wallace, M\. Mulvenna, and G\. Epelde \(2020\)Reliability of supervised machine learning using synthetic data in health care: model to preserve privacy for data sharing\.JMIR medical informatics8\(7\),pp\. e18910\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1)\.
- J\. Robinson, R\. Ranjan, W\. Hu, K\. Huang, J\. Han, A\. Dobles, M\. Fey, J\. E\. Lenssen, Y\. Yuan, Z\. Zhang, X\. He, and J\. Leskovec \(2024\)RelBench: a benchmark for deep learning on relational databases\.InAdvances in Neural Information Processing Systems,A\. Globerson, L\. Mackey, D\. Belgrave, A\. Fan, U\. Paquet, J\. Tomczak, and C\. Zhang \(Eds\.\),Vol\.37,pp\. 21330–21341\.External Links:[Document](https://dx.doi.org/10.52202/079017-0672),[Link](https://proceedings.neurips.cc/paper_files/paper/2024/file/25cd345233c65fac1fec0ce61d0f7836-Paper-Datasets_and_Benchmarks_Track.pdf)Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p2.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.4.2.1.3.1)\.
- A\. Saxena and K\. Goebel \(2008\)Turbofan engine degradation simulation data set\.Note:NASA Prognostics Data Repository, NASA Ames Research CenterExternal Links:[Link](https://data.nasa.gov/dataset/cmapss-jet-engine-simulated-data)Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p9.1)\.
- A\. V\. Solatorio and O\. Dupriez \(2023\)REaLTabFormer: generating realistic relational and tabular data using transformers\.External Links:2302\.02041,[Link](https://arxiv.org/abs/2302.02041)Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.15606#S4.SS1.p1.1)\.
- P\. Tiwald, I\. Krchova, A\. Sidorenko, M\. V\. Vieyra, M\. Scriminaci, and M\. Platzer \(2025\)Tabularargn: a flexible and efficient auto\-regressive framework for generating high\-fidelity synthetic data\.arXiv preprint arXiv:2501\.12012\.Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1),[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px2.p1.1),[Table 1](https://arxiv.org/html/2607.15606#S3.T1.3.1.1.1.1.1.1.3.7.2.1.3.1)\.
- P\. Wagner, N\. Strodthoff, R\. Bousseljot, W\. Samek, and T\. Schaeffter \(2022\)PTB\-XL, a large publicly available electrocardiography dataset\.PhysioNet\.Note:Version 1\.0\.3External Links:[Document](https://dx.doi.org/10.13026/kfzx-aw45),[Link](https://doi.org/10.13026/kfzx-aw45)Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p5.1)\.
- J\. Wilkes \(2011\)More Google cluster data\.Mountain View, CA, USA\.Note:Google research blogPosted at[http://googleresearch\.blogspot\.com/2011/11/more\-google\-cluster\-data\.html](http://googleresearch.blogspot.com/2011/11/more-google-cluster-data.html)\.Cited by:[§D\.4](https://arxiv.org/html/2607.15606#A4.SS4.p8.1)\.
- K\. Zhang, N\. Patki, and K\. Veeramachaneni \(2022a\)Sequential models in the synthetic data vault\.arXiv preprint arXiv:2207\.14406\.Cited by:[§2](https://arxiv.org/html/2607.15606#S2.SS0.SSS0.Px1.p1.1)\.
- K\. Zhang, N\. Patki, and K\. Veeramachaneni \(2022b\)Sequential models in the synthetic data vault\.arXiv preprint arXiv:2207\.14406\.Cited by:[§1](https://arxiv.org/html/2607.15606#S1.p1.1),[§1](https://arxiv.org/html/2607.15606#S1.p2.1)\.

Table 9\.Applicability Conditions, Feature Scope, and Representative Datasets for the Proposed Evaluation Metrics\.Scope: U = Univariate \(per feature, averaged\), B = Bivariate \(per feature pair, averaged\), M = Multivariate \(joint computation\)\. The “Applicable Features” column specifies which feature types each metric operates on\.A catalog table summarizing the applicability conditions and feature scope of the proposed evaluation metrics\. Rows are grouped by evaluation perspective, including timestamp, cross\-sectional, longitudinal, structural, and privacy metrics\. Columns describe each metric name, whether it is computed over univariate, bivariate, or multivariate feature scope, the applicable feature types, supported time representation, periodicity requirement, trajectory independence condition, and data\-structure requirement\. The table shows that the proposed metrics cover a broad range of temporal and relational settings, while some metrics require specific conditions such as absolute time, regular periodicity, dependent trajectories, or multi\-child relational structures\.

PerspectiveMetric NameScopeApplicable FeaturesTime Repr\.PeriodicityTraj\. Indep\.Data Str\.TimestampTimeIntervalDistributionSimilarityUxt​i​m​ex^\{time\}BothIrregularBothAllRegularityConsistencyUxt​i​m​ex^\{time\}BothBothBothAllTemporalRangeComplianceUxt​i​m​ex^\{time\}BothBothBothAllGridCompletenessUxt​i​m​ex^\{time\}BothRegularBothAllTemporalOrderConsistencyUxt​i​m​ex^\{time\}BothBothBothAllTimestampUniquenessUxt​i​m​ex^\{time\}BothBothBothAllTrajectoryDurationSimilarityUxt​i​m​ex^\{time\}BothBothBothAllCross\-sectionalCS\-KSComplementUEachxn​u​mx^\{num\}Abs\.BothDep\.All∗CS\-StatisticSimilarityUEachxn​u​mx^\{num\}Abs\.BothDep\.All∗CS\-RangeCoverageUEachxn​u​mx^\{num\}Abs\.BothDep\.All∗CS\-TVComplementUEachxc​a​tx^\{cat\}Abs\.BothDep\.All∗CS\-CategoryCoverageUEachxc​a​tx^\{cat\}Abs\.BothDep\.All∗CS\-CorrelationSimilarityBEach\(xan​u​m,xbn​u​m\)\(x^\{num\}\_\{a\},x^\{num\}\_\{b\}\)pairAbs\.BothDep\.All∗CS\-ContingencySimilarityBEach\(xac​a​t,xbc​a​t\)\(x^\{cat\}\_\{a\},x^\{cat\}\_\{b\}\)pairAbs\.BothDep\.All∗LongitudinalFirstDifferenceKSComplementUEachxn​u​mx^\{num\}BothRegularBothAllTransitionMatrixTVDComplementUEachxc​a​tx^\{cat\}BothRegularBothAllAutoCorrelationSimilarityUEachxn​u​mx^\{num\}Both†RegularBoth†AllTT\-WassersteinDistance \([Liet al\.](https://arxiv.org/html/2607.15606#bib.bib45)\)MAllxn​u​mx^\{num\}jointlyBothRegularBothAllMLD\-TS \([Garutiet al\.](https://arxiv.org/html/2607.15606#bib.bib6)\)MAll features at timettBothBothBothAllStruct\.SequenceLengthSimilarityUtrajectory lengthLkL\_\{k\}BothBothBothAllTemporalCardinalityShapeSimilarityUEach parent–child relationAbs\.BothBothM\-ChildDynamicKHopCorrelationSimilarityBCross\-table\(xa,xb\)\(x\_\{a\},x\_\{b\}\)pairAbs\.RegularDep\.M\-ChildPrivacyCS\-DCRMAll features at timettAbs\.BothDep\.AllCS\-NNDRMAll features at timettAbs\.BothDep\.Alln\-gramPrivacyMAll features at timettBothBothBothAllUtilityMLE\-TSMAll features at timettAbs\.BothBothAllMLE\-TemporalMAll features at timettAbs\.RegularBothAll

∗For multi\-table data only\.†Mode depends on trajectory independence\. Scope: U is per\-feature, B is per\-pair, and M is joint over all features; U and B are averaged\.

## Appendix AEvaluation Metrics

This appendix gives the operational definition of every metric used in the main paper\. All metrics produce a scalar in\[0,1\]\[0,1\]unless noted otherwise;11denotes perfect fidelity\. Notation follows Section[3\.1](https://arxiv.org/html/2607.15606#S3.SS1):TTandT^\\hat\{T\}are the real and synthetic tables,xk,jt​i​m​ex^\{time\}\_\{k,j\}is the timestamp of thejj\-th record of trajectorykk,Δ​tk,j=xk,jt​i​m​e−xk,j−1t​i​m​e\\Delta t\_\{k,j\}=x^\{time\}\_\{k,j\}\-x^\{time\}\_\{k,j\-1\},LkL\_\{k\}is trajectory length, andKKis the number of trajectories\.

### A\.1\.Feature Scope and Aggregation

Each metric operates at one of three scopes:univariate\(per feature columnff\),bivariate\(per feature pair\(f1,f2\)\(f\_\{1\},f\_\{2\}\)\), ormultivariate\(joint feature vector / trajectory embedding\)\. For univariate and bivariate metrics, the per\-feature \(or per\-pair\) score is averaged uniformly across the applicable setℱ\\mathcal\{F\}\(or𝒫\\mathcal\{P\}\): Applicable features per metric \(numerical only, categorical only, both\) are listed in the online appendix’s metric\-applicability table\.

### A\.2\.Timestamp Metrics

All timestamp metrics are computed on the*raw*synthetic output before sorting, deduplication, boundary trimming, or imputation, so generator\-level timestamp failures are not hidden by post\-processing\.

TemporalOrderConsistency\(TempOrderConsist; all series\) measures the fraction of consecutive timestamp pairs that are non\-decreasing:

\(1\)1−∑k∑j=2Lk𝕀​\(Δ​tsynth,k,j<0\)∑k\(Lk−1\)\.1\-\\frac\{\\sum\_\{k\}\\sum\_\{j=2\}^\{L\_\{k\}\}\\mathbb\{I\}\(\\Delta t\_\{\\mathrm\{synth\},k,j\}<0\)\}\{\\sum\_\{k\}\(L\_\{k\}\-1\)\}\.
TimestampUniqueness\(TimestampUnique; all series\) measures the fraction of consecutive intervals that are strictly positive, detecting duplicate timestamps before deduplication:

\(2\)1−∑k∑j=2Lk𝕀​\(Δ​tsynth,k,j=0\)∑k\(Lk−1\)\.1\-\\frac\{\\sum\_\{k\}\\sum\_\{j=2\}^\{L\_\{k\}\}\\mathbb\{I\}\(\\Delta t\_\{\\mathrm\{synth\},k,j\}=0\)\}\{\\sum\_\{k\}\(L\_\{k\}\-1\)\}\.
TemporalRangeCompliance\(TempRangeComp; all series\) measures the fraction of synthetic records within the valid real temporal domainΩreal\\Omega\_\{\\mathrm\{real\}\}; for relative time, the first timestamp must also be anchored at zero:

\(3\)1−1Nsynth​∑k∑jVk,j,1\-\\frac\{1\}\{N\_\{\\mathrm\{synth\}\}\}\\sum\_\{k\}\\sum\_\{j\}V\_\{k,j\},whereVk,jV\_\{k,j\}is the per\-record violation indicator\.

RegularityConsistency\(RegularityConsist; regular series only\) measures the fraction of synthetic intervals matching the canonical intervalccwithin toleranceϵ=0\.01​c\\epsilon=0\.01c:

\(4\)1−∑k∑j=2Lk𝕀​\(\|Δ​tsynth,k,j−c\|\>ϵ\)∑k\(Lk−1\)\.1\-\\frac\{\\sum\_\{k\}\\sum\_\{j=2\}^\{L\_\{k\}\}\\mathbb\{I\}\(\|\\Delta t\_\{\\mathrm\{synth\},k,j\}\-c\|\>\\epsilon\)\}\{\\sum\_\{k\}\(L\_\{k\}\-1\)\}\.
GridCompleteness\(GridCompleteness; regular series only\) compares real and synthetic canonical grid\-point multiplicities, capping synthetic credit at the real multiplicity:

\(5\)∑gmin⁡\(Mreal​\(g\),Msynth​\(g\)\)∑gMreal​\(g\)\.\\frac\{\\sum\_\{g\}\\min\(M\_\{\\mathrm\{real\}\}\(g\),M\_\{\\mathrm\{synth\}\}\(g\)\)\}\{\\sum\_\{g\}M\_\{\\mathrm\{real\}\}\(g\)\}\.
TimeIntervalDistributionSimilarity\(TimeIntervalDistrSim; irregular series only\) compares pooled real and synthetic inter\-arrival distributions using the KS complement:

\(6\)1−supΔ​t\|Freal​\(Δ​t\)−Fsynth​\(Δ​t\)\|\.1\-\\sup\_\{\\Delta t\}\\bigl\|F\_\{\\mathrm\{real\}\}\(\\Delta t\)\-F\_\{\\mathrm\{synth\}\}\(\\Delta t\)\\bigr\|\.
TrajectoryDurationSimilarity\(TrajDurationSim; all series\) compares real and synthetic trajectory\-duration distributions using the KS complement, withDk=xk,Lkt​i​m​e−xk,1t​i​m​eD\_\{k\}=x^\{time\}\_\{k,L\_\{k\}\}\-x^\{time\}\_\{k,1\}:

\(7\)1−supD\|Freal​\(D\)−Fsynth​\(D\)\|\.1\-\\sup\_\{D\}\\bigl\|F\_\{\\mathrm\{real\}\}\(D\)\-F\_\{\\mathrm\{synth\}\}\(D\)\\bigr\|\.

### A\.3\.Cross\-Sectional Metrics

Cross\-sectional metrics compare real and synthetic feature distributions within aligned temporal partitions\. They apply to datasets with*Absolute Time*and*Dependent Trajectories*\. LetΩ=⨆l=1BΩl\\Omega=\\bigsqcup\_\{l=1\}^\{B\}\\Omega\_\{l\}be a partition of the temporal domain, and letT\|lT\|\_\{l\}andT^\|l\\hat\{T\}\|\_\{l\}be records whose timestamps fall inΩl\\Omega\_\{l\}\. Any base measureμ\\muis lifted to a cross\-sectional metric as

\(8\)μC​S​\(T,T^\)=1B​∑l=1Bμ​\(T\|l,T^\|l\)\.\\mu\_\{CS\}\(T,\\hat\{T\}\)=\\frac\{1\}\{B\}\\sum\_\{l=1\}^\{B\}\\mu\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)\.For featureff,Tl\(f\)T\_\{l\}^\{\(f\)\}andT^l\(f\)\\hat\{T\}\_\{l\}^\{\(f\)\}denote values in partitionΩl\\Omega\_\{l\};FTl\(f\)F\_\{T\_\{l\}\}^\{\(f\)\}is the numerical CDF andPTl\(f\)P\_\{T\_\{l\}\}^\{\(f\)\}the categorical distribution\.

CS\-KSComplementcompares numerical distribution shapes within each time partition:

\(9\)μK​S​\(T\|l,T^\|l\)=1−supx\|FTl\(f\)​\(x\)−FT^l\(f\)​\(x\)\|\.\\mu^\{KS\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=1\-\\sup\_\{x\}\\left\|F\_\{T\_\{l\}\}^\{\(f\)\}\(x\)\-F\_\{\\hat\{T\}\_\{l\}\}^\{\(f\)\}\(x\)\\right\|\.
CS\-StatisticSimilaritycompares time\-local summary statisticsS∈\{mean,median,std\}S\\in\\\{\\mathrm\{mean\},\\mathrm\{median\},\\mathrm\{std\}\\\}:

\(10\)μSS​t​a​t​\(T\|l,T^\|l\)=1−\|S​\(Tl\(f\)\)−S​\(T^l\(f\)\)\|maxl′⁡S​\(Tl′\(f\)\)−minl′⁡S​\(Tl′\(f\)\)\+ϵ,\\mu^\{Stat\}\_\{S\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=1\-\\frac\{\\left\|S\(T\_\{l\}^\{\(f\)\}\)\-S\(\\hat\{T\}\_\{l\}^\{\(f\)\}\)\\right\|\}\{\\max\_\{l^\{\\prime\}\}S\(T\_\{l^\{\\prime\}\}^\{\(f\)\}\)\-\\min\_\{l^\{\\prime\}\}S\(T\_\{l^\{\\prime\}\}^\{\(f\)\}\)\+\\epsilon\},with the reported score averaged over the three statistics and clipped to\[0,1\]\[0,1\]\.

CS\-RangeCoveragemeasures whether synthetic numerical values remain inside the real range at each time partition:

\(11\)μR​a​n​g​e​\(T\|l,T^\|l\)=1\|T^l\(f\)\|​∑x∈T^l\(f\)𝕀​\[x∈\[min⁡Tl\(f\),max⁡Tl\(f\)\]\]\.\\mu^\{Range\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=\\frac\{1\}\{\|\\hat\{T\}\_\{l\}^\{\(f\)\}\|\}\\sum\_\{x\\in\\hat\{T\}\_\{l\}^\{\(f\)\}\}\\mathbb\{I\}\\\!\\left\[x\\in\\left\[\\min T\_\{l\}^\{\(f\)\},\\max T\_\{l\}^\{\(f\)\}\\right\]\\right\]\.
CS\-TVComplementcompares categorical distributions using the total variation complement:

\(12\)μT​V​\(T\|l,T^\|l\)=1−12​∑c\|PTl\(f\)​\(c\)−PT^l\(f\)​\(c\)\|\.\\mu^\{TV\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=1\-\\frac\{1\}\{2\}\\sum\_\{c\}\\left\|P\_\{T\_\{l\}\}^\{\(f\)\}\(c\)\-P\_\{\\hat\{T\}\_\{l\}\}^\{\(f\)\}\(c\)\\right\|\.
CS\-CategoryCoveragemeasures whether real categories at a time partition also appear in synthetic data:

\(13\)μC​a​t​C​o​v​\(T\|l,T^\|l\)=\|CTl\(f\)∩CT^l\(f\)\|\|CTl\(f\)\|,\\mu^\{CatCov\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=\\frac\{\|C\_\{T\_\{l\}\}^\{\(f\)\}\\cap C\_\{\\hat\{T\}\_\{l\}\}^\{\(f\)\}\|\}\{\|C\_\{T\_\{l\}\}^\{\(f\)\}\|\},where empty real partitions are excluded from the average\.

CS\-CorrelationSimilaritycompares numerical pairwise correlations within each time partition:

\(14\)μC​o​r​r​\(T\|l,T^\|l\)=1−\|ρTl​\(f1,f2\)−ρT^l​\(f1,f2\)\|2\.\\mu^\{Corr\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=1\-\\frac\{\|\\rho\_\{T\_\{l\}\}\(f\_\{1\},f\_\{2\}\)\-\\rho\_\{\\hat\{T\}\_\{l\}\}\(f\_\{1\},f\_\{2\}\)\|\}\{2\}\.
CS\-ContingencySimilaritycompares categorical co\-occurrence patterns using the TV complement over joint category frequencies:

\(15\)μC​o​n​t​\(T\|l,T^\|l\)=1−12​∑a∑b\|PTl\(f1,f2\)​\(a,b\)−PT^l\(f1,f2\)​\(a,b\)\|\.\\mu^\{Cont\}\(T\|\_\{l\},\\hat\{T\}\|\_\{l\}\)=1\-\\frac\{1\}\{2\}\\sum\_\{a\}\\sum\_\{b\}\\left\|P\_\{T\_\{l\}\}^\{\(f\_\{1\},f\_\{2\}\)\}\(a,b\)\-P\_\{\\hat\{T\}\_\{l\}\}^\{\(f\_\{1\},f\_\{2\}\)\}\(a,b\)\\right\|\.

### A\.4\.Longitudinal Metrics

Longitudinal metrics treat each entity as an ordered trajectory\. Step\-level metrics compare consecutive changes; trajectory\-level metrics compare longer range temporal structure\. Except forTT\-WassersteinDistanceand rawMLD\-TSdetection accuracy, larger values indicate better fidelity\.

FirstDifferenceKSComplement\(FirstDiffKSComplement; numerical\)\. Measures whether synthetic local increments match real increments, using pooled first differencesΔ​xk,j=xk,j−xk,j−1\\Delta x\_\{k,j\}=x\_\{k,j\}\-x\_\{k,j\-1\}:

\(16\)1−supδ\|FrealΔ​\(δ\)−FsynthΔ​\(δ\)\|\.1\-\\sup\_\{\\delta\}\\left\|F^\{\\Delta\}\_\{\\mathrm\{real\}\}\(\\delta\)\-F^\{\\Delta\}\_\{\\mathrm\{synth\}\}\(\\delta\)\\right\|\.Scores are computed per numerical feature and aggregated as described in Appendix[A\.1](https://arxiv.org/html/2607.15606#A1.SS1)\.

TransitionMatrixTVDComplement\(TransMatrixTVDComplement; categorical\)\. For category setCCand valid transition times𝒯\\mathcal\{T\},

\(17\)1−12​\|C\|​\|𝒯\|∑t∈𝒯∑i,j∈C\|Ptr\(j∣i\)−Pts\(j∣i\)\|\.1\-\\frac\{1\}\{2\|C\|\|\\mathcal\{T\}\|\}\\sum\_\{t\\in\\mathcal\{T\}\}\\sum\_\{i,j\\in C\}\\left\|P^\{r\}\_\{t\}\(j\\mid i\)\-P^\{s\}\_\{t\}\(j\\mid i\)\\right\|\.HerePtrP^\{r\}\_\{t\}andPtsP^\{s\}\_\{t\}denote real and synthetic transition probabilities; scores are averaged over categorical features\. Scores are computed per categorical feature and averaged\.

AutocorrelationSimilarity\(AutoCorrSimilarity; numerical\)\. Measures whether lag\-wise temporal dependence is preserved by comparing autocorrelation profiles up toH=min⁡\(L/4,50\)H=\\min\(L/4,50\):

\(18\)1−12​H​∑h=1H\|ρhreal−ρhsynth\|\.1\-\\frac\{1\}\{2H\}\\sum\_\{h=1\}^\{H\}\\left\|\\rho^\{\\mathrm\{real\}\}\_\{h\}\-\\rho^\{\\mathrm\{synth\}\}\_\{h\}\\right\|\.For independent trajectories, autocorrelation is computed per trajectory and averaged; for dependent trajectories with shared absolute time, it is computed on the cross\-sectional mean trajectory\.

MLD\-TS\(MLD\-TS; multivariate\)\. MLD\-TS evaluates whether real and synthetic trajectories are distinguishable by a supervised classifier\. Each trajectory is embedded aszk=ψ​\(T​\(k\)\)z\_\{k\}=\\psi\(T\(k\)\), labeled by source, and classified byhh; raw MLD\-TS is detection accuracy:

\(19\)1\|𝒟test\|​∑\(z,y\)∈𝒟test𝕀​\{h​\(z\)=y\}\.\\frac\{1\}\{\|\\mathcal\{D\}\_\{\\mathrm\{test\}\}\|\}\\sum\_\{\(z,y\)\\in\\mathcal\{D\}\_\{\\mathrm\{test\}\}\}\\mathbb\{I\}\\\{h\(z\)=y\\\}\.Values near chance indicate low distinguishability, while higher values indicate more detectable temporal mismatch\. Classifier settings are provided in Online Appendix D\.6\.

TT\-WassersteinDistance\(TT\-WassersteinDistance; multivariate\)\. TT\-Wasserstein compares the global distribution of trajectory patterns via spectral embeddings\. Each trajectoryX∈ℝLk×CX\\in\\mathbb\{R\}^\{L\_\{k\}\\times C\}is z\-score normalized, first\-differenced, and mapped to Fourier\-magnitude features:

\(20\)ϕ\(c\)​\(X\)=\|DFT​\(zt\(c\)−zt−1\(c\)\)1:F\|,ϕ​\(X\)=vec​\(\[ϕ\(1\),…,ϕ\(C\)\]\)\.\\phi^\{\(c\)\}\(X\)=\\bigl\|\\mathrm\{DFT\}\(z^\{\(c\)\}\_\{t\}\-z^\{\(c\)\}\_\{t\-1\}\)\_\{1:F\}\\bigr\|,\\qquad\\phi\(X\)=\\mathrm\{vec\}\(\[\\phi^\{\(1\)\},\\ldots,\\phi^\{\(C\)\}\]\)\.With costMi​j=‖ϕ​\(Xireal\)−ϕ​\(Xjsynth\)‖2M\_\{ij\}=\\\|\\phi\(X\_\{i\}^\{\\mathrm\{real\}\}\)\-\\phi\(X\_\{j\}^\{\\mathrm\{synth\}\}\)\\\|^\{2\},

\(21\)DTTW=\(minΓ∈Π​\(a,b\)​∑i,jΓi​j​Mi​j\)1/2\.D\_\{\\mathrm\{TTW\}\}=\\left\(\\min\_\{\\Gamma\\in\\Pi\(a,b\)\}\\sum\_\{i,j\}\\Gamma\_\{ij\}M\_\{ij\}\\right\)^\{1/2\}\.SmallerDTTWD\_\{\\mathrm\{TTW\}\}indicates better preservation of the trajectory distribution; it is reported as a distance rather than a\[0,1\]\[0,1\]similarity\.

### A\.5\.Structural Metrics

Structural metrics evaluate relational properties of sequential data; larger values indicate better structural fidelity\.

SequenceLengthSimilarity\(adopted from SDMetrics\(DataCebo, Inc\.,[2020](https://arxiv.org/html/2607.15606#bib.bib51)\); all schemas\) compares the real and synthetic trajectory\-length distributions:

\(22\)1−supL\|Freal​\(L\)−Fsynth​\(L\)\|\.1\-\\sup\_\{L\}\\left\|F\_\{\\mathrm\{real\}\}\(L\)\-F\_\{\\mathrm\{synth\}\}\(L\)\\right\|\.
TemporalCardinalityShapeSimilarity\(temporal extension of SyntheRela’s CardinalityShapeSimilarity\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\); multi\-child schemas\) compares the window\-level child\-record count distributions for each parent–child relation:

\(23\)1−sups\|Freal​\(s\)−Fsynth​\(s\)\|,1\-\\sup\_\{s\}\\left\|F\_\{\\mathrm\{real\}\}\(s\)\-F\_\{\\mathrm\{synth\}\}\(s\)\\right\|,wheressdenotes child\-record counts within aligned temporal windows\.

DynamicKHopCorrelationSimilarity\(temporal extension of SyntheRela’skk\-hop correlation similarity\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\); multi\-child schemas\) compares cross\-table correlations over time for variables linked by akk\-hop foreign\-key path:

\(24\)1−1\|𝕋eval\|​∑t∈𝕋eval\|ρreal​\(t\)−ρsynth​\(t\)\|2\.1\-\\frac\{1\}\{\|\\mathbb\{T\}\_\{\\mathrm\{eval\}\}\|\}\\sum\_\{t\\in\\mathbb\{T\}\_\{\\mathrm\{eval\}\}\}\\frac\{\|\\rho\_\{\\mathrm\{real\}\}\(t\)\-\\rho\_\{\\mathrm\{synth\}\}\(t\)\|\}\{2\}\.The score is averaged over applicablekk\-hop variable pairs, withk=1k=1by default\.

### A\.6\.Privacy and Utility Metrics

Privacy metrics evaluate three leakage granularities: row\-level proximity \(DCR,NNDR\), same\-time\-slice proximity \(CS\-DCR,CS\-NNDR\), and sequential\-pattern privacy \(NGP\(n\)\)\. Higher values are safer, except thatDCRandCS\-DCRare raw distances\. LetXreal\(i\)X^\{\(i\)\}\_\{\\rm real\}be the numerical feature vector of real recordii\.

DCRmeasures the median nearest\-neighbor distance from each real record to the synthetic table:

Mediani⁡\(minj⁡‖Xreal\(i\)−Xsynth\(j\)‖2\)\.\\operatorname\{Median\}\_\{i\}\\left\(\\min\_\{j\}\\left\\\|X^\{\(i\)\}\_\{\\mathrm\{real\}\}\-X^\{\(j\)\}\_\{\\mathrm\{synth\}\}\\right\\\|\_\{2\}\\right\)\.
NNDRis the median ratio between the first\- and second\-nearest synthetic neighbors of each real record; higher ratios imply fewer isolated near\-matches\.

CS\-DCRandCS\-NNDRrestrict the same nearest\-neighbor computations to records in the same timestamp or temporal partition:

Mediant∈𝕋eval⁡Mediani:xit​i​m​e=t⁡\(minj:x^jt​i​m​e=t⁡‖Xreal\(i\)−Xsynth\(j\)‖2\),\\operatorname\{Median\}\_\{t\\in\\mathbb\{T\}\_\{\\mathrm\{eval\}\}\}\\operatorname\{Median\}\_\{i:x^\{time\}\_\{i\}=t\}\\left\(\\min\_\{j:\\hat\{x\}^\{time\}\_\{j\}=t\}\\left\\\|X^\{\(i\)\}\_\{\\mathrm\{real\}\}\-X^\{\(j\)\}\_\{\\mathrm\{synth\}\}\\right\\\|\_\{2\}\\right\),withCS\-NNDRdefined analogously using same\-time\-slice first\- and second\-nearest neighbors\.

nn\-gramPrivacyNGP\(n\)measures whether discretized synthetic trajectory fragments reproduce real length\-nntoken subsequences:

\(25\)NgramExposure​\(n\)=1\|𝒦^\|​∑k∈𝒦^1\|Gk\(n\)\|​∑g∈Gk\(n\)𝕀​\(g∈𝒢real\(n\)\),\\mathrm\{NgramExposure\}\(n\)=\\frac\{1\}\{\|\\hat\{\\mathcal\{K\}\}\|\}\\sum\_\{k\\in\\hat\{\\mathcal\{K\}\}\}\\frac\{1\}\{\|G\_\{k\}^\{\(n\)\}\|\}\\sum\_\{g\\in G\_\{k\}^\{\(n\)\}\}\\mathbb\{I\}\\\!\\left\(g\\in\\mathcal\{G\}\_\{\\mathrm\{real\}\}^\{\(n\)\}\\right\),whereGk\(n\)G\_\{k\}^\{\(n\)\}is the set of synthetic length\-nntoken subsequences and𝒢real\(n\)\\mathcal\{G\}\_\{\\mathrm\{real\}\}^\{\(n\)\}is the real subsequence set\. We define

\(26\)NGP​\(n\)=1−NgramExposure​\(n\),\\mathrm\{NGP\}\(n\)=1\-\\mathrm\{NgramExposure\}\(n\),withNGP\(1\) andNGP\(3\) distinguishing single\-row from longer within\-trajectory sequential\-pattern reproduction\.

MLE\-TS\(MLE\-TS\)MLE\-TS uses the same protocol as MLD\-TS, but trains a downstream predictor instead of a detector\. For each trajectoryTa​\(k\)T^\{a\}\(k\),a∈\{real,synth\}a\\in\\\{\\mathrm\{real,synth\}\\\}, we computezka=ψ​\(Ta​\(k\)\)z\_\{k\}^\{a\}=\\psi\(T^\{a\}\(k\)\)and pair it with labelyky\_\{k\}\. A predictorfgf\_\{g\}trained on synthetic pairs is evaluated on held\-out real trajectories by

MLE​\-​TS​\(g\)=AUC​\(\{fg​\(zkreal\)\},\{ykreal\}\)\.\\mathrm\{MLE\\text\{\-\}TS\}\(g\)=\\mathrm\{AUC\}\\bigl\(\\\{f\_\{g\}\(z\_\{k\}^\{\\mathrm\{real\}\}\)\\\},\\\{y\_\{k\}^\{\\mathrm\{real\}\}\\\}\\bigr\)\.
MLE\-Temporal\(MLE\-Temporal\)MLE\-Temporal adapts the same train\-on\-synthetic, test\-on\-real protocol to record\-level prediction under a chronological split\. For each trajectoryTa​\(k\)T^\{a\}\(k\),a∈\{real,synth\}a\\in\\\{\\mathrm\{real,synth\}\\\}, and prediction timett, we computezk,ta=ψ​\(Ta​\(k\)≤t\)z\_\{k,t\}^\{a\}=\\psi\(T^\{a\}\(k\)\_\{\\leq t\}\)from the history observed up tottand pair it with labelyk,ty\_\{k,t\}\. A predictorfgf\_\{g\}trained on synthetic temporal pairs is evaluated on held\-out real pairs from later timestamps by

MLE​\-​Temporal​\(g\)=ℳ​\(\{fg​\(zk,treal\)\}\(k,t\)∈𝒟testreal,\{yk,treal\}\(k,t\)∈𝒟testreal\),\\mathrm\{MLE\\text\{\-\}Temporal\}\(g\)=\\mathcal\{M\}\\\!\\left\(\\\{f\_\{g\}\(z\_\{k,t\}^\{\\mathrm\{real\}\}\)\\\}\_\{\(k,t\)\\in\\mathcal\{D\}\_\{\\mathrm\{test\}\}^\{\\mathrm\{real\}\}\},\\\{y\_\{k,t\}^\{\\mathrm\{real\}\}\\\}\_\{\(k,t\)\\in\\mathcal\{D\}\_\{\\mathrm\{test\}\}^\{\\mathrm\{real\}\}\}\\right\),whereℳ\\mathcal\{M\}is AUC for classification andR2R^\{2\}for regression\. It measures whether synthetic data preserve task\-relevant historical dynamics for time\-ordered record\-level prediction\.

## Appendix BTaxonomy: Formal Definitions

Temporal Characteristics\.Observations withAbsolute Timeoperate on a globally shared calendar domain𝕋g​l​o​b​a​l\\mathbb\{T\}\_\{global\}, so simultaneous events across trajectories share the same temporal reference:xk,jt​i​m​e∈𝕋g​l​o​b​a​lx^\{time\}\_\{k,j\}\\in\\mathbb\{T\}\_\{global\}\. InRelative Time, each trajectory operates on its own lifecycle timeline, with the first observation normalized to zero:xk,1t​i​m​e=0​∀kx^\{time\}\_\{k,1\}=0\\ \\forall k\. ARegularseries has a fixed inter\-arrival intervalcc:Δ​tk,j=c​∀k,j\\Delta t\_\{k,j\}=c\\ \\forall k,j\. AnIrregularseries has stochastic inter\-arrival times drawn from a distributionP​\(Δ​t\)P\(\\Delta t\):Δ​tk,j∼P​\(Δ​t\)\\Delta t\_\{k,j\}\\sim P\(\\Delta t\)\.

Trajectory Dynamics\.Independenttrajectories represent entirely isolated entities; the trajectory of one carries no information about another:P​\(T​\(k\),T​\(k′\)\)=P​\(T​\(k\)\)​P​\(T​\(k′\)\)P\(T\(k\),T\(k^\{\\prime\}\)\)=P\(T\(k\)\)\\,P\(T\(k^\{\\prime\}\)\)for anyk≠k′k\\neq k^\{\\prime\}\.Dependenttrajectories share macro\-level dynamics, so their trajectories are statistically correlated:∃k≠k′\\exists\\,k\\neq k^\{\\prime\}s\.t\.P​\(T​\(k\),T​\(k′\)\)≠P​\(T​\(k\)\)​P​\(T​\(k′\)\)P\(T\(k\),T\(k^\{\\prime\}\)\)\\neq P\(T\(k\)\)\\,P\(T\(k^\{\\prime\}\)\)\. Evaluating trajectory dependencies requires Absolute Time, as a globally shared axis is a prerequisite for aligning observations across trajectories\.

Structural Complexity\.We characterize relational schemas by the number of 1:N foreign\-key relationships each row participates in\. Given parent tableTpT\_\{p\}, child tableTcT\_\{c\}, and FK mapfF​K:Tc→Tpf\_\{FK\}:T\_\{c\}\\to T\_\{p\}, the child set of a parent row is𝒞​\(𝐫p\)=\{𝐫c∈Tc∣fF​K​\(𝐫c\)=𝐫p\}\\mathcal\{C\}\(\\mathbf\{r\}\_\{p\}\)=\\\{\\mathbf\{r\}\_\{c\}\\in T\_\{c\}\\mid f\_\{FK\}\(\\mathbf\{r\}\_\{c\}\)=\\mathbf\{r\}\_\{p\}\\\}\. We distinguish four schema typesSingle\(no external FK; trajectory in one table\),Linear\(∀𝐫p,∃\!⁡Tc\\forall\\,\\mathbf\{r\}\_\{p\},\\,\\exists\!\\,T\_\{c\}:𝒞​\(𝐫p\)⊆Tc\\mathcal\{C\}\(\\mathbf\{r\}\_\{p\}\)\\subseteq T\_\{c\}\),Multi\-Child\(𝒞\(m\)​\(𝐫p\)⊆Tcm\\mathcal\{C\}^\{\(m\)\}\(\\mathbf\{r\}\_\{p\}\)\\subseteq T\_\{c\_\{m\}\}form∈\{1,…,M\}m\\in\\\{1,\\ldots,M\\\},M≥2M\{\\geq\}2\), andMulti\-Parent\(fF​K\(m\)​\(𝐫c\)=𝐫pm∈Tpmf\_\{FK\}^\{\(m\)\}\(\\mathbf\{r\}\_\{c\}\)=\\mathbf\{r\}\_\{p\_\{m\}\}\\in T\_\{p\_\{m\}\}form∈\{1,…,M\}m\\in\\\{1,\\ldots,M\\\},M≥2M\{\\geq\}2\)\. This schema axis introduces relational consistency as an additional evaluation requirement beyond temporal fidelity and determines which structural sub\-metrics apply to each dataset\.

## Appendix CTemporal Post\-processing Pipeline Overview

As discussed in the main paper, we apply a deterministic five\-stage pipeline to repair temporal violations \(e\.g\., chronological ordering, calendar alignment\) before computing non\-timestamp metrics\. Figure[5](https://arxiv.org/html/2607.15606#A3.F5)provides a comprehensive visual overview of this sequence, illustrating how raw synthetic outputs are progressively sorted, aligned, trimmed, deduplicated, and optionally imputed\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x5.png)Figure 5\.Detailed overview of the temporal post\-processing pipeline\. This deterministic five\-stage process is applied to generative model outputs before non\-timestamp fidelity evaluation\.A pipeline diagram showing the temporal post\-processing process applied to raw synthetic data before non\-timestamp fidelity evaluation\. The pipeline first records timestamp metrics before processing, then applies five stages in order: chronological sorting, time representation alignment, temporal boundary trimming, deduplication, and selective imputation\. Green stages are always applied, the orange stage which is only for stage 5 is applied only to regular time\-series data, and the blue box indicates pre\-pipeline timestamp metric recording\. The processed data are then used for cross\-sectional, longitudinal, structural, and privacy evaluation\.### C\.1\.Detailed Pipeline Stages

Generative models that treat timestamps as ordinary features frequently emit outputs that violate the preconditions assumed by non\-timestamp metrics: chronological ordering, calendar alignment, and gap\-free trajectories\. We apply a deterministic five\-stage pipeline to repair these violations before computing non\-timestamp metrics; timestamp metrics, by contrast, are computed on the raw synthetic output so that violations are not masked by the corrections themselves\. At each stage we log the intervention ratioρs=\(Nsmod\+Nsdrop\)/Nsin\\rho\_\{s\}=\(N^\{\\text\{mod\}\}\_\{s\}\+N^\{\\text\{drop\}\}\_\{s\}\)/N^\{\\text\{in\}\}\_\{s\}, the fraction of records modified or dropped, as an auxiliary signal of temporal\-coherence failure\.

##### Stages \(in dependency order\)\.

\(1\) Sort: records sorted ascending by\(xk​e​y,xt​i​m​e\)\(x^\{key\},x^\{time\}\)\.\(2\) Time Alignment: synthetic timestamps snapped to the canonical grid at intervalcc; non\-calendar outputs are anchored at the earliest real period and assignedcc\-spaced increments\.\(3\) Temporal Boundary Trimming: records outside the observed support\[Tmin,Tmax\]\[T\_\{\\min\},T\_\{\\max\}\]are removed\.\(4\) Deduplication: duplicate\(xk​e​y,xt​i​m​e\)\(x^\{key\},x^\{time\}\)pairs are resolved by retaining the first occurrence\.\(5\) Selective Imputation\(regular series only\): unoccupied grid points within each trajectory’s observed range are filled according to the chosen variant; points outside this range are not imputed\.

##### Method variants\.

Stages \(1\)–\(4\) are deterministic; the four variants differ only in Stage \(5\)’s imputation:sparse\(default; insert asNaN, exposing the model’s coverage pattern as a measurable property\);id\-fill\(within\-trajectory mean/mode\);prev\-fill\(forward\-fill, backward\-fill for leading gaps\);interp\-fill\(linear interpolation for numerical, forward/backward fill for categorical\)\.

### C\.2\.Recommended Configurations

Among the pipeline steps, only Stages \(2\) and \(5\) require configuration\. For Stage 2, calendar\-aligned synthetic timestamps are anchored to canonical period boundaries \(e\.g\., first day of the month\) rather than nearest\-neighbor rounding, guaranteeing membership in the grid required byGridCompleteness\. For Stage 5, we strongly recommend thesparsevariant as the default\. Standard imputations \(id\-fill,prev\-fill,interp\-fill\) inject in\-distribution values, mechanically inflating fidelity scores and concealing a model’s failure to maintain temporal coverage\. While these fill variants serve as useful ablation baselines for evaluating feature\-level fidelity*conditional*on complete coverage \(detailed in Section[D\.2](https://arxiv.org/html/2607.15606#A4.SS2)\), the intervention ratioρ5\\rho\_\{5\}must always be reported alongside metric scores to ensure transparency\.

## Appendix DExperimental Details

### D\.1\.Baseline Training Setup & Hardware

To ensure fair reproducibility, all generative models were trained using default hyperparameters and configurations from their official repositories or the SyntheRela benchmark\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\)\. For baseline dataset preprocessing, we applied a uniform pipeline: numerical missing values were mean\-imputed \(rounded for integers\), categorical gaps were filled with a placeholder \(‘?’\), and hash\-based IDs were globally integerized to maintain relational integrity\. Excessively large datasets were subsampled at the trajectory \(primary key\) level for computational feasibility\. All experiments were executed on a server equipped with NVIDIA RTX 6000 Ada GPUs\.

### D\.2\.Imputation Sensitivity Analysis

We conduct an ablation study to empirically validate that the choice of imputation strategy \(Stage 5\) does not materially alter the comparative conclusions drawn from Seq2Synth\. Specifically, we compare four variants —sparse\(default, missing grid points left asNaN\),id\-fill\(within\-trajectory mean/mode\),prev\-fill\(forward\-fill with backward\-fill for leading gaps\), andinterp\-fill\(linear interpolation for numerical; forward/backward fill for categorical\) — across representative regular datasets, Rossmann and Walmart\. Imputation variants are applicable only to regular\-series datasets; for irregular\-series datasets \(Airbnb, Berka\) and the PTB\-XL ECG dataset, which involve independent trajectories or sparse event structures, the evaluation reduces to thesparsebaseline and a single “default” point is shown\.

##### Protocol\.

For each datasetdd, metric groupm∈\{SD,CS,Long,Struct\}m\\in\\\{\\text\{SD\},\\text\{CS\},\\text\{Long\},\\text\{Struct\}\\\}, and imputation variantvv, we compute each model’s*rank*\(1 = best\) within the set of evaluated models\. Model ranks are then tracked across imputation variants\. A stable rank profile indicates that the relative ordering of models — and thus the benchmark’s comparative conclusions — is insensitive to the imputation choice\.

##### Results\.

Figure[6](https://arxiv.org/html/2607.15606#A4.F6)shows model ranks per dataset and metric group under all applicable imputation variants\. The key observation is that rank orderings remain largely stable across variants for the majority of dataset–metric combinations\. Rank crossings, when they occur, are almost exclusively between models that are already closely ranked under the default setting, reflecting genuine measurement noise rather than a systematic artefact of imputation\. No imputation variant consistently elevates or demotes a specific model across datasets, and models that rank near the top \(or bottom\) undersparsetend to maintain their relative position under all three fill\-based alternatives\.

This stability holds across both feature\-sensitive metric groups \(Cross\-Sectional, Longitudinal\) and structure\-sensitive ones \(Structural\), indicating that the effect of filling missing grid points with in\-distribution values does not substantially inflate or suppress any model’s score relative to its competitors\. The result is consistent with our theoretical expectation: because all models are subject to the same imputation procedure, the filling introduces a uniform bias that cancels in comparative analysis\.

For irregular\-series and independent\-trajectory datasets \(PTB\-XL\), which are evaluated only undersparse, ranks are determined solely by the model’s ability to generate the correct temporal support, confirming that imputation is not a confound for these data types\.

##### Implications\.

These results jointly support two claims\. First, thesparsedefault is empirically justified: adopting any of the three fill\-based alternatives leads to the same comparative conclusions while introducing unnecessary feature\-level bias as discussed in Section[C\.2](https://arxiv.org/html/2607.15606#A3.SS2)\. Second, the metrics themselves are robust: they quantify genuine model\-level differences in temporal fidelity rather than artefacts of the post\-processing pipeline\. Together, these findings validate both the imputation design choice and the metric computations reported in the main paper\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/x6.png)Figure 6\.Model ranks under different post\-processing imputation variants on Rossmann and Walmart\. Each colored line traces one model across imputation variants\. The rank ordering is largely stable across default sparse insertion, ID\-fill, previous\-fill, and interpolation\-fill variants, suggesting that the choice of imputation strategy has limited impact on comparative model evaluation\.A line\-plot figure showing model ranks across post\-processing imputation variants\. The x\-axis lists imputation variants, including default, ID\-fill, previous\-fill, and interpolation\-fill, and the y\-axis reports model rank with 1 as the best rank\. Each colored line represents a synthetic data generation model\. The visible panels show Rossmann and Walmart under the longitudinal metric group\. Most lines remain flat or change only slightly across variants, indicating that model rankings are largely stable under different imputation strategies\.

### D\.3\.Detailed Dataset Statistics

To provide a comprehensive operational overview of our evaluation testbed, Table[10](https://arxiv.org/html/2607.15606#A4.T10)summarizes the structural dimensions of the 13 sequential tabular datasets, including the total number of relational tables, absolute rows, schema columns, unique entity trajectories, and the resulting average trajectory length\.

Table 10\.Detailed Statistics of Sequential Tabular DatasetsA statistics table summarizing the sequential tabular datasets used in the benchmark\. Each row corresponds to a dataset, and columns report the number of tables, rows, columns, trajectories, and average trajectory length\. The table shows substantial variation in dataset scale and temporal structure, ranging from small datasets with a few dozen trajectories to large datasets with hundreds of thousands of rows or long average trajectories\.Dataset\# tables\# rows\# columns\# trajectoriesavg traj\. lengthWalmart315,3172045334\.38PTB\-XL2101,000351,000100FreddieMAC2536,5783943,96611\.20FannieMAE22,992,78247183,77715\.28H&M3297,8793610,00024\.03Coupon5259,8333822,8735\.41Google5756,167474981,019\.20Home Credit71,263,30021810,00036\.35Rossmann213,8262022361\.00AirBnB240,281321,94219\.74Berka245,6661990049\.74CMAPSS1160,35926709226\.18Citi Bike1559,644155,79396\.61

### D\.4\.Per\-Dataset Description

We evaluate our benchmark on a diverse set of real\-world sequential tabular datasets, selected to cover a wide range of temporal characteristics, relational structures, and application domains\.

WalmartWe use the subsampled versions of Walmart and Rossmann datasets used in SyntheRela\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\)\. Both datasets exhibit regular, absolute timestamps with fixed\-length trajectories\.

H&M Personalized Fashion Recommendations\.H&M\(H&M Group,[2021](https://arxiv.org/html/2607.15606#bib.bib36)\)contains customer purchase records over time, along with auxiliary information on users and items\. It features a relational schema with two parent tables and one child table, posing challenges for models that cannot handle multi\-parent dependencies \(e\.g\., RTF\)\.

Coupon Purchase Prediction\.The Coupon dataset\(haisland0909et al\.,[2015](https://arxiv.org/html/2607.15606#bib.bib43)\)includes user profiles, coupon metadata, browsing logs, and purchase events\. It has a multi\-parent, multi\-child relational structure with 2\-hop dependencies, making it suitable for evaluating relational consistency across multiple tables\.

PTB\-XL\.PTB\-XL\(Wagneret al\.,[2022](https://arxiv.org/html/2607.15606#bib.bib39)\)consists of electrocardiography \(ECG\) signals collected at high temporal resolution\. It is suitable for evaluating synthetic data generation in the healthcare domain, where privacy preservation and realistic temporal modeling are critical\. Each record forms a fixed\-length time series, allowing evaluation of models on dense and high\-frequency temporal data\.

Freddie Mac and Fannie MAE\.The Freddie Mac dataset\(Freddie Mac,[2026](https://arxiv.org/html/2607.15606#bib.bib46)\)provides loan\-level mortgage performance data spanning multiple decades while Fannie MAE\(Fannie Mae,[2026](https://arxiv.org/html/2607.15606#bib.bib47)\)contains detailed records of single\-family mortgage loans\.

Home Credit Default Risk\.The Home Credit dataset\(Home Credit Group,[2018](https://arxiv.org/html/2607.15606#bib.bib40)\)provides transactional and application data for credit risk prediction\. Notably, the application table contains over 120 features, allowing evaluation of high\-dimensional tabular generation\.

Google Cluster Traces v2\.This dataset\(Wilkes,[2011](https://arxiv.org/html/2607.15606#bib.bib42)\)records task execution traces from a large\-scale cluster system\. Time is represented in relative units \(600\-second intervals\), and each task forms a temporal sequence, enabling evaluation under system\-level workload dynamics\.

CMAPSS\.CMAPSS\(Saxena and Goebel,[2008](https://arxiv.org/html/2607.15606#bib.bib41)\)is a simulated dataset of aircraft engine degradation trajectories\. Each sequence evolves over relative time cycles, making it suitable for evaluating temporal progression and failure patterns\.

Citi Bike NYC\.The Citi Bike dataset\(Citi Bike NYC,[2013](https://arxiv.org/html/2607.15606#bib.bib44)\)contains trip\-level records with absolute timestamps\. Each trajectory corresponds to a bike usage session, allowing evaluation of real\-world mobility patterns with irregular temporal spacing\.

AirBnB, Berka and RossmannThe AirBnB dataset\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)includes temporally ordered reservation records together with static listing attributes, enabling evaluation of models on relational data with heterogeneous temporal patterns and sparse event occurrences\. The Berka dataset\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)is a financial relational dataset consisting of customer accounts, transactions, loans, and demographic information\. Transaction histories evolve over absolute time and exhibit long\-term sequential dependencies, making the dataset suitable for evaluating temporal consistency and relational coherence in synthetic financial records\. The Rossmann dataset\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)contains daily sales records from retail stores along with static store metadata and promotion\-related information\. Each store forms a fixed\-frequency temporal trajectory with regular daily intervals, allowing evaluation of seasonal patterns, trend preservation, and long\-range temporal dependencies in retail forecasting scenarios\.

### D\.5\.Preprocessing Details per Dataset

Baseline missing\-value preprocessing is described in Section[D\.1](https://arxiv.org/html/2607.15606#A4.SS1); temporal post\-processing is described in Section[C](https://arxiv.org/html/2607.15606#A3)\.

##### Retail Domain\.

We utilize the subsampled version Walmart provided by SyntheRela\(Jurkovicet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib22)\)\. For Rossmann, AirBnB, and Berka, we consider test\-set splits that authors of TabDiT\(Garutiet al\.,[2025](https://arxiv.org/html/2607.15606#bib.bib6)\)provided are used as the real datasets for evaluating all seven baseline models, while TabDiT\-generated samples are directly used\. For H&M, we randomly subsample 10,000 customers from the original customer IDs\. Image\-related information is excluded, and only the corresponding subsampled article metadata is retained in the articles table\.

##### Medical Domain\.

PTB\-XL is preprocessed using the official pipeline provided by the source dataset and then decomposed into a parent\-child relational structure, where metadata is stored in the parent table and ECG signals are stored in the child table\. We use the 100Hz recordings, for which eachecg\_idoriginally contains 1,000 temporal observations\. Since generated data may not reliably preserve microsecond\-level temporal precision, we introduce a relative timestep column \(step\) to represent temporal ordering explicitly\. We further apply temporal downsampling to reduce each trajectory to 100 timesteps for more stable and computationally efficient benchmarking\. A total of 1,000ecg\_ids are randomly subsampled\. Columns with high missing\-value ratios are removed to improve robustness\.

##### Finance Domain\.

For Freddie Mac and Fannie Mae, we use loan records reported after 2024\. In the case of Fannie Mae, the original single\-table structure is transformed into a relational schema by separating static loan attributes into a parent table and time\-varying records into a child table\. For Home Credit Default Risk, 10,000 IDs are randomly subsampled from the full dataset\.

##### Other Domains\.

For Google Cluster Traces v2, we use the first five shards and randomly subsample 500 machine IDs\. To establish a relational schema with a designated primary entity, static job\-level attributes are separated from event logs to construct a root table namedjobs\. This restructuring is not applicable to machine events because they contain only static information; therefore, the machine events and machine attribute tables are excluded\. For CMAPSS, the four simulation subsets are merged into a single unified table\.

### D\.6\.MLD\-TS and MLE\-TS Evaluation Details

Table 11\.XGBoost hyperparameter grid, with one configuration sampled per seed\.A table listing the XGBoost hyperparameter search grid used in the utility evaluation\. The table includes four hyperparameters: maximum tree depth, learning rate, minimum child weight, and number of estimators\. One configuration is sampled from the listed candidate values for each experimental seed\.HyperparameterValuemax\_depth\{3,5,7,9\}\\\{3,5,7,9\\\}learning\_rate\{0\.01,0\.03,0\.05,0\.10\}\\\{0\.01,0\.03,0\.05,0\.10\\\}min\_child\_weight\{1,3\}\\\{1,3\\\}n\_estimators\{50\}\\\{50\\\}We used XGBoost\(Chen and Guestrin,[2016](https://arxiv.org/html/2607.15606#bib.bib35)\)for both MLD\-TS and MLE\-TS evaluations\. In MLD\-TS, real and synthetic samples were combined and then split into training and test sets with a ratio of 8:2\. The model was trained as a binary classifier to distinguish real samples from synthetic samples, and accuracy was used as the evaluation metric\. In MLE\-TS, the training set was constructed using only synthetic data, while the test set consisted only of real data, following the same 8:2 split ratio\. For each random seed, hyperparameters were randomly sampled from a predefined search space summarized in Table[11](https://arxiv.org/html/2607.15606#A4.T11)\.

##### Downstream Tasks for MLE\-TS\.

Since MLE\-TS evaluates whether synthetic data preserves the predictive structure of real data, it requires a target label for each sample\. For datasets where the original target label is not directly available, we define binary prediction tasks using attributes from the corresponding parent, store, customer, or entity\-level tables\. Specifically:

- •In Airbnb, we define the taskn\_sessions\_ge\_17\. The target label is set to 1 ifn\_sessionsis greater than or equal to 17, and 0 otherwise\.
- •In Berka, we define the taskregion\_is\_moravia\. The target label is set to 1 if the customer’s region is either South Moravia or North Moravia, and 0 otherwise\.
- •In Citi Bike, we define the taskmode\_gender\_is\_1\. For each bike, we compute the mode ofgenderacross its records and set the target label to 1 if the modal value is 1, and 0 otherwise\.
- •In CMAPSS, we define the taskfinal\_s11\_high\_regime\. For each unit, we use the value ofs\_11at the final time step and predict whether it is greater than or equal to the median value computed from the real data\.
- •In Coupon, we define the tasksex\_is\_m\. The target label is set to 1 ifsexis male, and 0 otherwise\.
- •In Fannie Mae, and Freddie Mac, we define the taskproperty\_type\_is\_4\. The target label is set to 1 if the corresponding property\-type field is equal to 4, and 0 otherwise\.
- •In Google Cluster, we define the taskscheduling\_class\_ge\_2\. The target label is set to 1 ifscheduling\_classis greater than or equal to 2, and 0 otherwise\.
- •In H&M, we use the binary attributefashion\_news\_regularlyas the target label\.
- •In Home Credit, we use the binary attributeTARGETas the target label\.
- •In PTB\-XL, we use the binary attributesexas the target label\.
- •In Rossmann, we use the binary attributePromo2from the store table\. The target label is set to 1 ifPromo2is equal to 1, and 0 otherwise\.
- •In Walmart, we define the taskstore\_type\_is\_A\. The target label is set to 1 if the store typeTypeis “A”, and 0 otherwise\.

## Appendix EAdditional Results

### E\.1\.Results on Additional Dataset

Additional results on single\-table and complex datasets\.Tables[12](https://arxiv.org/html/2607.15606#A5.T12)and[13](https://arxiv.org/html/2607.15606#A5.T13)report the remaining dataset\-level results beyond the seven core datasets\.

Table 12\.Results for single table datasetsA results table reporting fidelity scores for single\-table datasets, Citi Bike and CMAPSS\. Rows compare synthetic data generation models, and columns report five evaluation dimensions: statistical distribution, timestamp fidelity, cross\-sectional fidelity, longitudinal fidelity, and structural fidelity\. Scores range from zero to one, with higher values indicating better fidelity\. The table shows that model performance differs across the two single\-table datasets and across temporal fidelity dimensions\.ModelCiti BikeCMAPSSsdtscslgstsdtscslgstClavaDDPM0\.990\\mathbf\{0\.990\}0\.769¯\\underline\{0\.769\}0\.941\\mathbf\{0\.941\}0\.965¯\\underline\{0\.965\}0\.9080\.9630\.575–0\.4710\.709CPAR0\.7060\.7210\.6140\.8110\.2710\.8110\.969\\mathbf\{0\.969\}–0\.573¯\\underline\{0\.573\}0\.836RCTGAN0\.943¯\\underline\{0\.943\}0\.7650\.900¯\\underline\{0\.900\}0\.9600\.979\\mathbf\{0\.979\}0\.8130\.369–0\.4590\.330RTF0\.8700\.6780\.8850\.967\\mathbf\{0\.967\}0\.6760\.972¯\\underline\{0\.972\}0\.322–0\.618\\mathbf\{0\.618\}0\.000SDV0\.8830\.782\\mathbf\{0\.782\}0\.8480\.9500\.979\\mathbf\{0\.979\}0\.9160\.545–0\.4250\.961\\mathbf\{0\.961\}TabARGN0\.8900\.2010\.7570\.9210\.1540\.983\\mathbf\{0\.983\}0\.578¯\\underline\{0\.578\}–0\.4850\.917¯\\underline\{0\.917\}

The single\-table datasets confirm that temporal fidelity remains multi\-dimensional even without explicit inter\-table relationships\. On Citi Bike, ClavaDDPM leads static and cross\-sectional fidelity, RTF leads longitudinal fidelity, and RCTGAN/SDV achieve the strongest structural scores\. On CMAPSS, TabularARGN obtains the best static\-distribution score, whereas CPAR, RTF, and SDV lead timestamp, longitudinal, and structural fidelity, respectively\. Thus, even in single\-table settings, no single dimension summarizes overall temporal quality\.

Table 13\.Results for complex datasetsA results table reporting fidelity scores for four complex datasets: Coupon, Google Cluster, H&M, and Home Credit\. Rows compare synthetic data generation models, and columns report statistical distribution, timestamp fidelity, cross\-sectional fidelity, longitudinal fidelity, and structural fidelity\. Scores range from zero to one, with higher values indicating better fidelity\. The table shows that model rankings vary substantially across complex relational and temporal datasets, indicating that performance depends on both data structure and fidelity dimension\.

ModelCouponGoogle ClustersdtscslgstsdtscslgstClavaDDPM0\.895¯\\underline\{0\.895\}0\.8280\.801\\mathbf\{0\.801\}0\.6360\.9740\.863¯\\underline\{0\.863\}0\.604–0\.4810\.977RCTGAN0\.8940\.8170\.798¯\\underline\{0\.798\}0\.6260\.9300\.7150\.574–0\.4570\.708RDBDiff0\.976\\mathbf\{0\.976\}0\.896\\mathbf\{0\.896\}0\.7890\.6680\.987\\mathbf\{0\.987\}0\.935\\mathbf\{0\.935\}0\.627–0\.507¯\\underline\{0\.507\}1\.000\\mathbf\{1\.000\}RGCLD0\.8630\.6060\.7370\.6740\.9490\.7060\.650\\mathbf\{0\.650\}–0\.516\\mathbf\{0\.516\}0\.986RelDiff0\.8810\.848¯\\underline\{0\.848\}0\.7790\.908\\mathbf\{0\.908\}0\.979¯\\underline\{0\.979\}0\.7810\.645¯\\underline\{0\.645\}–0\.4551\.000\\mathbf\{1\.000\}SDV0\.8270\.8050\.4740\.837¯\\underline\{0\.837\}0\.8950\.5990\.630–0\.4860\.567

ModelH&MHome CreditsdtscslgstsdtscslgstClavaDDPM0\.933\\mathbf\{0\.933\}0\.6800\.6800\.8200\.8200\.873¯\\underline\{0\.873\}0\.640¯\\underline\{0\.640\}0\.6710\.6710\.6280\.628–0\.9160\.9160\.9530\.953RCTGAN0\.6260\.709\\mathbf\{0\.709\}0\.5210\.7150\.5550\.8500\.611–0\.8880\.870RDBDiff0\.891¯\\underline\{0\.891\}0\.6820\.7890\.7560\.6380\.896\\mathbf\{0\.896\}0\.690–0\.935¯\\underline\{0\.935\}0\.996¯\\underline\{0\.996\}RGCLD0\.8710\.704¯\\underline\{0\.704\}0\.874\\mathbf\{0\.874\}0\.876\\mathbf\{0\.876\}0\.6400\.860¯\\underline\{0\.860\}0\.719\\mathbf\{0\.719\}–0\.937\\mathbf\{0\.937\}0\.994RelDiff0\.8710\.6880\.842¯\\underline\{0\.842\}0\.7720\.6400\.8260\.671–0\.9101\.000\\mathbf\{1\.000\}SDV0\.6410\.5810\.4560\.6800\.648\\mathbf\{0\.648\}–––––

The complex\-schema datasets further amplify this pattern\. On Coupon, RDBDiff dominates static, timestamp, and structural fidelity, while RelDiff achieves the best longitudinal score\. On Google Cluster, diffusion\-based relational models preserve structural consistency well, but their longitudinal scores remain moderate\. On H&M and Home Credit, graph\- and diffusion\-based methods such as RGCLD, RDBDiff, and RelDiff generally perform strongly, but the best model still changes across dimensions\. These results show that complex schemas introduce additional failure modes: preserving relational structure does not guarantee faithful timestamp generation or trajectory evolution, and static\-distribution fidelity remains insufficient as a proxy for temporal quality\.

Table 14\.Per\-dataset fidelity scores across all benchmark datasets and five evaluation dimensions\. All scores lie in\[0,1\]\[0,1\], with higher values indicating better fidelity\. “–” denotes inapplicable cases\. Bold and underline mark the best and second\-best scores per dataset–metric row\.DatasetMetricClavaDDPMRCTGANRDBDiffRelDiffRGCLDRTFSDVTabDiTCPARTabARGNRossmannsd0\.8500\.8100\.858¯\\underline\{0\.858\}0\.7990\.8210\.8090\.7340\.932\\mathbf\{0\.932\}––ts0\.6070\.5620\.6080\.6020\.5980\.823¯\\underline\{0\.823\}0\.5650\.824\\mathbf\{0\.824\}––cs0\.912¯\\underline\{0\.912\}0\.8080\.912¯\\underline\{0\.912\}0\.8170\.8970\.8820\.6350\.965\\mathbf\{0\.965\}––lg0\.9170\.8720\.9150\.8820\.9020\.948¯\\underline\{0\.948\}0\.7890\.975\\mathbf\{0\.975\}––st1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}––Berkasd0\.9480\.8650\.992\\mathbf\{0\.992\}0\.8980\.9220\.951¯\\underline\{0\.951\}0\.6950\.909––ts0\.5940\.6200\.7590\.6030\.7310\.907\\mathbf\{0\.907\}0\.5350\.777¯\\underline\{0\.777\}––cs0\.691¯\\underline\{0\.691\}0\.6320\.829\\mathbf\{0\.829\}0\.6260\.6710\.6650\.4480\.651––lg0\.8770\.8580\.949\\mathbf\{0\.949\}0\.8680\.8850\.896¯\\underline\{0\.896\}0\.6860\.890––st0\.9930\.9521\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9930\.9520\.8140\.958––Fannie Maesd0\.900¯\\underline\{0\.900\}0\.8600\.8760\.8990\.906\\mathbf\{0\.906\}0\.8540\.814–––ts0\.5670\.5500\.571¯\\underline\{0\.571\}0\.598\\mathbf\{0\.598\}0\.5030\.4740\.481–––cs0\.965\\mathbf\{0\.965\}0\.8520\.8700\.8490\.876¯\\underline\{0\.876\}0\.7770\.772–––lg0\.8200\.7870\.7810\.8220\.858¯\\underline\{0\.858\}0\.8040\.864\\mathbf\{0\.864\}–––st0\.998\\mathbf\{0\.998\}0\.9530\.8220\.7500\.990¯\\underline\{0\.990\}0\.8170\.848–––Walmartsd0\.7960\.8610\.8150\.898¯\\underline\{0\.898\}0\.950\\mathbf\{0\.950\}0\.7190\.857–––ts0\.610\\mathbf\{0\.610\}0\.5260\.608¯\\underline\{0\.608\}0\.5980\.6000\.4550\.522–––cs0\.8670\.7850\.896\\mathbf\{0\.896\}0\.8280\.891¯\\underline\{0\.891\}0\.6050\.746–––lg0\.887\\mathbf\{0\.887\}0\.8440\.8680\.8520\.872¯\\underline\{0\.872\}0\.6900\.814–––st0\.8640\.7310\.887\\mathbf\{0\.887\}0\.8040\.882¯\\underline\{0\.882\}0\.5180\.786–––Airbnbsd0\.967\\mathbf\{0\.967\}0\.9090\.963¯\\underline\{0\.963\}0\.9370\.9250\.8790\.7110\.923––ts0\.875\\mathbf\{0\.875\}0\.8400\.8240\.860¯\\underline\{0\.860\}0\.8430\.7770\.8110\.860¯\\underline\{0\.860\}––cs––––––––––lg0\.9640\.970\\mathbf\{0\.970\}0\.9650\.969¯\\underline\{0\.969\}0\.969¯\\underline\{0\.969\}0\.9670\.9090\.965––st0\.9870\.9241\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9810\.6310\.9380\.912––PTB\-XLsd0\.886¯\\underline\{0\.886\}0\.5760\.896\\mathbf\{0\.896\}0\.6690\.6920\.6250\.758–––ts0\.5940\.3300\.5770\.5910\.5341\.000\\mathbf\{1\.000\}0\.675¯\\underline\{0\.675\}–––cs––––––––––lg0\.927\\mathbf\{0\.927\}0\.8410\.9090\.922¯\\underline\{0\.922\}0\.9060\.9150\.920–––st1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9991\.000\\mathbf\{1\.000\}–––Freddie Macsd0\.9440\.8820\.986\\mathbf\{0\.986\}0\.9200\.975¯\\underline\{0\.975\}0\.8530\.810–––ts0\.7130\.6880\.6600\.752\\mathbf\{0\.752\}0\.7360\.5810\.747¯\\underline\{0\.747\}–––cs0\.9240\.8430\.982\\mathbf\{0\.982\}0\.8470\.930¯\\underline\{0\.930\}0\.7770\.740–––lg0\.8420\.7970\.915\\mathbf\{0\.915\}0\.8410\.875¯\\underline\{0\.875\}0\.7840\.780–––st0\.9950\.9721\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9930\.6950\.965–––Couponsd0\.895¯\\underline\{0\.895\}0\.8940\.976\\mathbf\{0\.976\}0\.8810\.863–0\.827–––ts0\.8280\.8170\.896\\mathbf\{0\.896\}0\.848¯\\underline\{0\.848\}0\.606–0\.805–––cs0\.801\\mathbf\{0\.801\}0\.798¯\\underline\{0\.798\}0\.7890\.7790\.737–0\.474–––lg0\.6360\.6260\.6680\.908\\mathbf\{0\.908\}0\.674–0\.837¯\\underline\{0\.837\}–––st0\.9740\.9300\.987\\mathbf\{0\.987\}0\.979¯\\underline\{0\.979\}0\.949–0\.895–––Google Clustersd0\.863¯\\underline\{0\.863\}0\.7150\.935\\mathbf\{0\.935\}0\.7810\.706–0\.599–––ts0\.6040\.5740\.6270\.645¯\\underline\{0\.645\}0\.650\\mathbf\{0\.650\}–0\.630–––cs––––––––––lg0\.4810\.4570\.507¯\\underline\{0\.507\}0\.4550\.516\\mathbf\{0\.516\}–0\.486–––st0\.9770\.7081\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.986–0\.567–––H&Msd0\.933\\mathbf\{0\.933\}0\.6260\.891¯\\underline\{0\.891\}0\.8710\.871–0\.641–––ts0\.6800\.709\\mathbf\{0\.709\}0\.6820\.6880\.704¯\\underline\{0\.704\}–0\.581–––cs0\.8200\.5210\.7890\.842¯\\underline\{0\.842\}0\.874\\mathbf\{0\.874\}–0\.456–––lg0\.873¯\\underline\{0\.873\}0\.7150\.7560\.7720\.876\\mathbf\{0\.876\}–0\.680–––st0\.640¯\\underline\{0\.640\}0\.5550\.6380\.640¯\\underline\{0\.640\}0\.640¯\\underline\{0\.640\}–0\.648\\mathbf\{0\.648\}–––Home Creditsd0\.6710\.8500\.896\\mathbf\{0\.896\}0\.8260\.860¯\\underline\{0\.860\}–––––ts0\.6280\.6110\.690¯\\underline\{0\.690\}0\.6710\.719\\mathbf\{0\.719\}–––––cs––––––––––lg0\.9160\.8880\.935¯\\underline\{0\.935\}0\.9100\.937\\mathbf\{0\.937\}–––––st0\.9530\.8700\.996¯\\underline\{0\.996\}1\.000\\mathbf\{1\.000\}0\.994–––––Citi Bikesd0\.990\\mathbf\{0\.990\}0\.943¯\\underline\{0\.943\}–––0\.8700\.883–0\.7060\.890ts0\.769¯\\underline\{0\.769\}0\.765–––0\.6780\.782\\mathbf\{0\.782\}–0\.7210\.201cs0\.941\\mathbf\{0\.941\}0\.900¯\\underline\{0\.900\}–––0\.8850\.848–0\.6140\.757lg0\.965¯\\underline\{0\.965\}0\.960–––0\.967\\mathbf\{0\.967\}0\.950–0\.8110\.921st0\.9080\.979\\mathbf\{0\.979\}–––0\.6760\.979\\mathbf\{0\.979\}–0\.2710\.154CMAPSSsd0\.9630\.813–––0\.972¯\\underline\{0\.972\}0\.916–0\.8110\.983\\mathbf\{0\.983\}ts0\.5750\.369–––0\.3220\.545–0\.969\\mathbf\{0\.969\}0\.578¯\\underline\{0\.578\}cs––––––––––lg0\.4710\.459–––0\.618\\mathbf\{0\.618\}0\.425–0\.573¯\\underline\{0\.573\}0\.485st0\.7090\.330–––0\.0000\.961\\mathbf\{0\.961\}–0\.8360\.917¯\\underline\{0\.917\}
### E\.2\.MLE\-TS

Table 15\.AUC for MLE\-TS\. Original denotes the real\-data baseline trained and evaluated on real data\. Higher values indicate better downstream temporal utility, and the best synthetic result for each dataset is highlighted in bold\.A downstream utility table reporting AUC scores for the MLE\-TS task across all datasets\. Rows correspond to datasets, and columns compare the real\-data baseline with synthetic data generation models\. Higher AUC values indicate better downstream temporal utility, and the best synthetic result for each dataset is highlighted\. The table shows that temporal utility varies substantially by dataset and model, with some synthetic models approaching or matching the real\-data baseline on certain datasets while performing much worse on others\.DatasetOriginalClavaDDPMCPARRCTGANRTFSDVRDBDIFFRGCLDRelDiffTABARGNTabDiTRossmann0\.8060\.8060\.7710\.771–0\.3140\.3140\.5000\.5000\.5330\.5330\.7490\.7490\.7780\.7780\.7080\.708–0\.782\\mathbf\{0\.782\}Berka0\.5020\.5020\.4450\.445–0\.4800\.4800\.5110\.5110\.4670\.4670\.4920\.4920\.5500\.5500\.557\\mathbf\{0\.557\}–0\.4380\.438Fannie Mae0\.6850\.6850\.6010\.601–0\.5330\.5330\.6280\.6280\.6020\.6020\.6220\.6220\.6540\.6540\.658\\mathbf\{0\.658\}––Walmart0\.7170\.7170\.867\\mathbf\{0\.867\}–0\.5500\.5500\.7670\.7670\.7330\.7330\.8330\.8330\.7920\.7920\.5000\.500––Airbnb1\.0001\.0000\.8060\.806–0\.8810\.8810\.6240\.6240\.9780\.9781\.000\\mathbf\{1\.000\}1\.0001\.0000\.9300\.930–1\.000\\mathbf\{1\.000\}PTB\-XL0\.7120\.7120\.4730\.473–0\.4760\.4760\.672\\mathbf\{0\.672\}0\.5000\.5000\.5150\.5150\.5240\.5240\.4460\.446––Freddie Mac0\.6910\.6910\.4860\.486–0\.5190\.5190\.5720\.5720\.5000\.5000\.5040\.5040\.664\\mathbf\{0\.664\}0\.5960\.596––Citi Bike0\.9940\.9940\.9950\.9950\.996\\mathbf\{0\.996\}0\.8390\.8390\.9950\.9950\.8360\.836–––0\.6690\.669–CMAPSS0\.8480\.8480\.7570\.7570\.5000\.5000\.4750\.4750\.7570\.7570\.820\\mathbf\{0\.820\}–––0\.7710\.771–Coupon0\.6790\.6790\.5770\.577–0\.5070\.507–0\.5270\.5270\.5420\.5420\.645\\mathbf\{0\.645\}0\.6100\.610––Google Cluster0\.9500\.9500\.8280\.828–0\.6160\.616–0\.4370\.4370\.885\\mathbf\{0\.885\}0\.7900\.7900\.7250\.725––H&M0\.6020\.6020\.585\\mathbf\{0\.585\}–0\.4790\.479–0\.5360\.5360\.5790\.5790\.5770\.5770\.5740\.574––Home Credit0\.5900\.5900\.4670\.467–0\.4600\.460––0\.5170\.5170\.573\\mathbf\{0\.573\}0\.5300\.530––

Table[15](https://arxiv.org/html/2607.15606#A5.T15)summarizes downstream temporal utility on the MLE\-TS benchmark\. The best synthetic generators often approach, and sometimes surpass, the real\-data baseline, showing that synthetic data can support downstream temporal prediction when it preserves task\-relevant patterns rather than only marginal distributions\. At the same time, utility remains highly dataset\-dependent: no method consistently dominates, and larger gaps on datasets with complex temporal dynamics and heterogeneous feature interactions suggest that current generators still struggle to reproduce fine\-grained predictive structure\. This highlights the need to evaluate synthetic data not only by distributional fidelity, but also by whether it transfers useful temporal signals to downstream tasks\.

### E\.3\.MLE\-Temporal

Table 16\.MLE\-Temporal utility results across datasets\. Bold and underlined scores indicate the best and second\-best results within each dataset, respectively\.MLE\-Temporal utility results across four datasets\. AUC is reported for Fannie Mae and Freddie Mac, while $R^\{2\}$ is reported for Rossmann and Walmart\. Bold and underlined scores indicate the best and second\-best results within each dataset, respectively\.DatasetMetricModelPerformanceRossmannR2R^\{2\}ClavaDDPM0\.577R2R^\{2\}RCTGAN0\.422R2R^\{2\}RDBDIFF0\.530R2R^\{2\}RTF0\.285R2R^\{2\}RelDiff0\.187R2R^\{2\}RGCLD0\.571R2R^\{2\}SDV−64\.945\-64\.945R2R^\{2\}TabDiT0\.578Fannie MaeAUCClavaDDPM0\.502AUCRCTGAN0\.702AUCRDBDIFF0\.781AUCRTF0\.852AUCRelDiff0\.924AUCRGCLD0\.890AUCSDV0\.913WalmartR2R^\{2\}ClavaDDPM0\.355R2R^\{2\}RCTGAN0\.247R2R^\{2\}RDBDIFF0\.475R2R^\{2\}RTF0\.104R2R^\{2\}RelDiff−0\.014\-0\.014R2R^\{2\}RGCLD0\.516R2R^\{2\}SDV0\.012Freddie MacAUCClavaDDPM0\.596AUCRCTGAN0\.643AUCRDBDIFF0\.686AUCRTF0\.527AUCRelDiff0\.848AUCRGCLD0\.869AUCSDV0\.500Table[16](https://arxiv.org/html/2607.15606#A5.T16)reports MLE\-Temporal results under a chronological train/test split, where models are trained on earlier observations and evaluated on later ones\. This setting provides a stricter test than the random\-split MLE\-TS protocol because synthetic data must support forward\-looking temporal prediction\. On the binary classification tasks, RelDiff and RGCLD obtain the best AUC scores on Fannie Mae and Freddie Mac, respectively, with SDV also performing strongly on Fannie Mae\. In contrast, the regression tasks show weaker utility: the bestR2R^\{2\}values on Rossmann and Walmart remain moderate, and some generators produce near\-zero or negative scores\. This contrast suggests that current generators can preserve coarse temporal signals useful for classification more reliably than the fine\-grained continuous dynamics required for temporal forecasting\.

### E\.4\.MLD\-TS

Table 17\.Test accuracy for MLD\-TS\. child denotes the setting where only the child table is used, while merged denotes the setting where the child table is merged with the parent table\. Bold and underline indicate the lowest and second\-lowest detection results among synthetic generators, respectively\.A detection\-accuracy table for the MLD\-TS task across all benchmark datasets\. Each dataset has two settings: child, where only the child table is used, and merged, where the child table is merged with the parent table\. Columns compare the original real\-data baseline with synthetic data generation models\. Lower detection accuracy for synthetic generators indicates that synthetic data are harder to distinguish from real data and therefore more realistic under this detection task\. The table shows that most synthetic generators are still detected with high accuracy, while the lowest and second\-lowest synthetic detection results vary across datasets and settings\.DatasetSettingOriginalClavaDDPMCPARRCTGANRTFSDVRDBDIFFRGCLDRelDiffTABARGNTabDiTAirbnbchild0\.5030\.5030\.9640\.964–0\.9870\.9870\.8970\.8971\.0001\.0000\.9880\.9880\.8790\.8790\.8890\.889–0\.852\\mathbf\{0\.852\}merged0\.4990\.4990\.9650\.965–0\.9870\.9870\.9290\.9291\.0001\.0000\.9870\.9870\.879\\mathbf\{0\.879\}0\.9120\.912–0\.9470\.947Berkachild0\.4980\.4980\.9640\.964–0\.9900\.9900\.6720\.6720\.9990\.9990\.532\\mathbf\{0\.532\}0\.7380\.7380\.9880\.988–0\.8620\.862merged0\.4930\.4930\.9650\.965–0\.9900\.9900\.6690\.6690\.9990\.9990\.523\\mathbf\{0\.523\}0\.7410\.7410\.9880\.988–0\.8610\.861Citi Bikechild0\.4990\.4990\.804\\mathbf\{0\.804\}1\.0001\.0000\.9700\.9700\.9560\.9560\.9970\.997–––0\.9920\.992–merged0\.4990\.4990\.804\\mathbf\{0\.804\}1\.0001\.0000\.9700\.9700\.9560\.9560\.9970\.997–––0\.9920\.992–CMAPSSchild0\.5020\.5020\.9970\.9971\.0001\.0000\.9970\.9970\.976\\mathbf\{0\.976\}0\.9980\.998–––0\.9810\.981–merged0\.5020\.5020\.9970\.9971\.0001\.0000\.9970\.9970\.976\\mathbf\{0\.976\}0\.9980\.998–––0\.9810\.981–Couponchild0\.4990\.4990\.8420\.842–0\.8780\.878–0\.9650\.9650\.758\\mathbf\{0\.758\}0\.8120\.8120\.8810\.881––merged0\.4980\.4980\.8410\.841–0\.8790\.879–0\.9650\.9650\.759\\mathbf\{0\.759\}0\.8080\.8080\.8810\.881––Fannie Maechild0\.4990\.4991\.0001\.000–1\.0001\.0000\.838\\mathbf\{0\.838\}1\.0001\.0001\.0001\.0001\.0001\.0001\.0001\.000––merged0\.5000\.5001\.0001\.000–1\.0001\.0000\.840\\mathbf\{0\.840\}1\.0001\.0001\.0001\.0001\.0001\.0001\.0001\.000––Freddie Macchild0\.5020\.5021\.0001\.000–1\.0001\.0000\.9990\.9991\.0001\.0001\.0001\.0000\.966\\mathbf\{0\.966\}0\.9960\.996––merged0\.5020\.5021\.0001\.000–1\.0001\.0000\.9990\.9991\.0001\.0001\.0001\.0000\.966\\mathbf\{0\.966\}0\.9960\.996––Google Clusterchild0\.5030\.5030\.9640\.964–0\.9960\.996–0\.9990\.9990\.9150\.9150\.798\\mathbf\{0\.798\}0\.9760\.976––merged0\.5000\.5000\.9650\.965–0\.9960\.996–0\.9990\.9990\.9150\.9150\.802\\mathbf\{0\.802\}0\.9760\.976––H&Mchild0\.4950\.4950\.7340\.734–0\.9860\.986–1\.0001\.0000\.9030\.9030\.712\\mathbf\{0\.712\}0\.7360\.736––merged0\.4960\.4960\.735\\mathbf\{0\.735\}–0\.9860\.986–1\.0001\.0000\.9030\.9030\.9020\.9020\.9070\.907––Home Creditchild0\.4960\.4960\.9280\.928–0\.9190\.919––0\.9990\.9990\.691\\mathbf\{0\.691\}0\.8120\.812––merged0\.4970\.4971\.0001\.000–0\.9810\.981––0\.9990\.9990\.732\\mathbf\{0\.732\}0\.8490\.849––PTB\-XLchild0\.5010\.5011\.0001\.000–1\.0001\.0001\.0001\.0001\.0001\.0000\.858\\mathbf\{0\.858\}0\.9880\.9880\.9940\.994––merged0\.4910\.4911\.0001\.000–1\.0001\.0001\.0001\.0001\.0001\.0000\.861\\mathbf\{0\.861\}0\.9940\.9940\.9940\.994––Rossmannchild0\.5020\.5020\.9970\.997–0\.9850\.9850\.9840\.9840\.9970\.9970\.9860\.9860\.9840\.9840\.9980\.998–0\.825\\mathbf\{0\.825\}merged0\.5040\.5040\.9970\.997–0\.9900\.9900\.9840\.9840\.9970\.9970\.9850\.9850\.9860\.9860\.9980\.998–0\.817\\mathbf\{0\.817\}Walmartchild0\.5480\.5480\.9890\.989–0\.9890\.9890\.9820\.9820\.9890\.9890\.9780\.9780\.970\\mathbf\{0\.970\}0\.9890\.989––merged0\.5330\.5330\.9890\.989–0\.9890\.9890\.9820\.9820\.9890\.9890\.9780\.9780\.970\\mathbf\{0\.970\}0\.9890\.989––

Table[17](https://arxiv.org/html/2607.15606#A5.T17)reports the detection accuracy of the MLD\-TS classifier across all datasets, for both the child setting \(child table only\) and the merged setting \(child joined with parent attributes\)\. Lower accuracy indicates that real and synthetic records are harder to distinguish, and therefore that the synthetic data better reproduce the joint structure of the real records\. The real\-data baseline lies near0\.50\.5across all datasets, confirming that the classifier is not exploiting trivial artifacts\. In contrast, most synthetic generators are detected with accuracy well above0\.950\.95, indicating that current methods still leave clear distributional fingerprints under a learned discriminator\. A few exceptions show measurable progress: RDBDIFF on Berka achieves the lowest detection accuracy \(0\.5230\.523in the merged setting\), and TabDiT on Rossmann \(0\.8170\.817\) and Airbnb \(0\.8520\.852in the child setting\) likewise approach the lower end of the detectability range\. RGCLD performs best on several relational datasets \(H&M, Home Credit, Walmart\), consistent with its competitive temporal fidelity scores reported earlier\. Differences between the child and merged settings are generally small, indicating that the detector primarily relies on child\-table content rather than on parent–child interactions, and that synthetic\-vs\-real distinguishability is concentrated in the temporal records themselves\. Overall, while MLD\-TS confirms that recent relational and temporal generators have narrowed the realism gap on certain datasets, the gap to the real\-data baseline remains large, suggesting that distinguishability under learned discriminators is still an open challenge\.

### E\.5\.Privacy: Per\-Dataset Results

Table 18\.Privacy metric profiles on the six additional core datasets\. Convention: higher values indicate safer behavior\.DCRandCS\-DCRare raw median nearest\-neighbor distances \(not normalized\);NGP​\(n\)=1−NgramExposure​\(n\)∈\[0,1\]\\texttt\{NGP\}\(n\)=1\-\\texttt\{NgramExposure\}\(n\)\\in\[0,1\]\. Bold and underline mark the best and second\-best per column*within each dataset block*\.A single combined results table reporting privacy metric profiles across six datasets \(Berka, Airbnb, PTB\-XL, Fannie Mae, Freddie Mac, Walmart\)\. Each dataset block lists synthetic data generation models as rows\. Columns report row\-level privacy \(DCR, NNDR\), cross\-sectional privacy \(CS\-DCR, CS\-NNDR\), and n\-gram privacy \(NGP\(1\), NGP\(3\)\)\. Bold and underline mark the best and second\-best per column within each dataset block\. The table shows that privacy behavior differs across models and datasets, with models varying in their row\-level, time\-slice\-level, and temporal\-pattern privacy risks\.DatasetModelDCRCS\-DCRNNDRCS\-NNDRNGP\(1\)NGP\(3\)BerkaClavaDDPM47\.0647\.06576157610\.6850\.6850\.6000\.6000\.0010\.0010\.8880\.888RCTGAN51\.5051\.509919¯\\underline\{9919\}0\.7180\.7180\.6560\.6560\.0890\.0890\.9540\.954RDBDiff43\.9243\.92291929190\.6770\.6770\.4610\.4610\.0010\.0010\.5310\.531RTF49\.3849\.38910691060\.6900\.6900\.679¯\\underline\{0\.679\}0\.0060\.0060\.2850\.285RGCLD48\.3648\.36782078200\.6860\.6860\.6690\.6690\.6640\.6640\.9910\.991RelDiff54\.50¯\\underline\{54\.50\}866986690\.6920\.6920\.6530\.6530\.688¯\\underline\{0\.688\}0\.999¯\\underline\{0\.999\}SDV𝟑𝟐𝟕𝟔𝟖\\mathbf\{32768\}𝟒𝟑𝟖𝟑𝟏\\mathbf\{43831\}1\.000\\mathbf\{1\.000\}0\.905\\mathbf\{0\.905\}0\.996\\mathbf\{0\.996\}1\.000\\mathbf\{1\.000\}TabDiT49\.4049\.40809480940\.729¯\\underline\{0\.729\}0\.6730\.6730\.6440\.6440\.9880\.988AirbnbClavaDDPM0\.0000\.00010\.4710\.470\.5000\.5000\.4950\.4950\.0780\.0780\.9590\.959RCTGAN0\.0000\.00015\.9715\.970\.5000\.5000\.512\\mathbf\{0\.512\}0\.2020\.2020\.994¯\\underline\{0\.994\}RDBDiff0\.0000\.00011\.4611\.460\.5000\.5000\.4940\.4940\.2320\.2320\.7730\.773RTF0\.0000\.00012\.0212\.020\.5000\.5000\.5090\.5090\.0780\.0780\.8010\.801RGCLD0\.0000\.00010\.7810\.780\.5000\.5000\.4950\.4950\.1250\.1250\.7670\.767RelDiff0\.0000\.00017\.1017\.100\.5000\.5000\.510¯\\underline\{0\.510\}0\.285¯\\underline\{0\.285\}0\.9390\.939SDV1\.000\\mathbf\{1\.000\}501\.6\\mathbf\{501\.6\}0\.545¯\\underline\{0\.545\}0\.4880\.4881\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}TabDiT0\.0000\.00043\.07¯\\underline\{43\.07\}0\.635\\mathbf\{0\.635\}0\.5030\.5030\.1330\.1330\.7140\.714PTB\-XLClavaDDPM0\.0590\.0590\.1100\.1100\.9040\.9040\.9010\.9010\.0260\.0260\.7780\.778RCTGAN0\.317\\mathbf\{0\.317\}0\.722\\mathbf\{0\.722\}0\.927¯\\underline\{0\.927\}0\.8390\.8390\.986\\mathbf\{0\.986\}1\.000\\mathbf\{1\.000\}RDBDiff0\.0510\.0510\.1010\.1010\.8780\.8780\.8830\.8830\.0180\.0180\.2290\.229RTF0\.0640\.0640\.1150\.1150\.9210\.9210\.915¯\\underline\{0\.915\}0\.0700\.0700\.3270\.327RGCLD0\.0640\.0640\.1170\.1170\.9200\.9200\.9130\.9130\.0360\.0360\.2380\.238RelDiff0\.125¯\\underline\{0\.125\}0\.195¯\\underline\{0\.195\}0\.944\\mathbf\{0\.944\}0\.935\\mathbf\{0\.935\}0\.354¯\\underline\{0\.354\}0\.885¯\\underline\{0\.885\}SDV0\.0950\.0950\.1690\.1690\.927¯\\underline\{0\.927\}0\.9090\.9090\.1440\.1440\.7600\.760Fannie MaeClavaDDPM45\.9345\.93101\.7101\.70\.808¯\\underline\{0\.808\}0\.7750\.7750\.2880\.2881\.000\\mathbf\{1\.000\}RCTGAN68\.3768\.37353\.7353\.70\.7780\.7780\.7170\.7170\.979\\mathbf\{0\.979\}1\.000\\mathbf\{1\.000\}RDBDiff152\.5152\.5782\.0782\.00\.7810\.7810\.7340\.7340\.7040\.7041\.000\\mathbf\{1\.000\}RTF26\.5126\.5168\.8668\.860\.857\\mathbf\{0\.857\}0\.789¯\\underline\{0\.789\}0\.4210\.4211\.000\\mathbf\{1\.000\}RGCLD179\.7¯\\underline\{179\.7\}802\.4¯\\underline\{802\.4\}0\.7650\.7650\.7250\.7250\.4270\.4270\.9660\.966RelDiff82\.7582\.75300\.9300\.90\.7930\.7930\.7330\.7330\.8130\.8131\.000\\mathbf\{1\.000\}SDV456\.1\\mathbf\{456\.1\}𝟐𝟎𝟗𝟗\\mathbf\{2099\}0\.808¯\\underline\{0\.808\}0\.796\\mathbf\{0\.796\}0\.969¯\\underline\{0\.969\}1\.000\\mathbf\{1\.000\}Freddie MacClavaDDPM14\.6114\.6145\.0445\.040\.797¯\\underline\{0\.797\}0\.6970\.6970\.0050\.0050\.999\\mathbf\{0\.999\}RCTGAN198\.6\\mathbf\{198\.6\}𝟏𝟑𝟔𝟒\\mathbf\{1364\}0\.7380\.7380\.725¯\\underline\{0\.725\}0\.3020\.3020\.997¯\\underline\{0\.997\}RDBDiff16\.6116\.6155\.1655\.160\.7900\.7900\.7040\.7040\.0040\.0040\.5730\.573RTF31\.0831\.0871\.9771\.970\.7800\.7800\.7150\.7150\.517¯\\underline\{0\.517\}0\.997¯\\underline\{0\.997\}RGCLD42\.0642\.06185\.2185\.20\.7600\.7600\.7230\.7230\.0160\.0160\.6400\.640RelDiff135\.8135\.8641\.2¯\\underline\{641\.2\}0\.7410\.7410\.7190\.7190\.1610\.1610\.8920\.892SDV138\.7¯\\underline\{138\.7\}421\.5421\.50\.814\\mathbf\{0\.814\}0\.788\\mathbf\{0\.788\}0\.616\\mathbf\{0\.616\}0\.9280\.928WalmartClavaDDPM42\.5042\.5038\.4138\.410\.5350\.5350\.5460\.5461\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}RCTGAN822\.5822\.51495¯\\underline\{1495\}0\.669¯\\underline\{0\.669\}0\.639¯\\underline\{0\.639\}0\.5120\.5121\.000\\mathbf\{1\.000\}RDBDiff99\.4399\.43158\.8158\.80\.5510\.5510\.5290\.5291\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}RTF779\.4779\.4718\.7718\.70\.6510\.6510\.673\\mathbf\{0\.673\}0\.5100\.5100\.9640\.964RGCLD541\.1541\.1703\.1703\.10\.6450\.6450\.6360\.6360\.4610\.4611\.000\\mathbf\{1\.000\}RelDiff860\.9¯\\underline\{860\.9\}141514150\.674\\mathbf\{0\.674\}0\.639¯\\underline\{0\.639\}0\.5450\.5451\.000\\mathbf\{1\.000\}SDV𝟏𝟒𝟐𝟎\\mathbf\{1420\}𝟐𝟗𝟗𝟎\\mathbf\{2990\}0\.5590\.5590\.6030\.6030\.5160\.5161\.000\\mathbf\{1\.000\}

Table[18](https://arxiv.org/html/2607.15606#A5.T18)report privacy metric on the remaining six datasets to complement the Rossmann analysis in Section[4\.2](https://arxiv.org/html/2607.15606#S4.SS2.SSS0.Px3)\. All six metrics follow the*higher\-is\-safer*convention;DCRandCS\-DCRare raw median nearest\-neighbor distances and are not normalized\. For thenn\-gram metric we reportNGP​\(n\)=1−NgramExposure​\(n\)\\texttt\{NGP\}\(n\)=1\-\\texttt\{NgramExposure\}\(n\), so values close to11indicate that the synthetic data reproduce few real length\-nnsubsequences\.

##### Cross\-sectional restriction\.

Across the six datasets,CS\-DCRexceedsDCRon roughly90%90\\%of model–dataset pairs, confirming that the row\-level closeness signal is dominated by neighbors at unrelated time slices\. The ratio varies sharply with dataset characteristics: on Berka \(long, irregular financial trajectories\) the median inflation is∼160×\\sim\\\!160\\times, on Fannie Mae and Freddie Mac \(loan histories\)∼3\\sim\\\!3–5×5\\times, and on PTB\-XL \(short fixed\-length ECG sequences\) only∼1\.8×\\sim\\\!1\.8\\times\. Walmart is the partial exception: ClavaDDPM hasCS\-DCR=38\.4<DCR=42\.5\\texttt\{CS\-DCR\}\\\!=\\\!38\.4<\\texttt\{DCR\}\\\!=\\\!42\.5and RTF hasCS\-DCR=718\.7<DCR=779\.4\\texttt\{CS\-DCR\}\\\!=\\\!718\.7<\\texttt\{DCR\}\\\!=\\\!779\.4, meaning that same\-week nearest neighbors are closer on average than time\-agnostic ones—an instance where the row\-level metric understates rather than overstates time\-aligned identifiability\.

##### nn\-gram Privacy\.

Then=1n\{=\}1vs\.n=3n\{=\}3disagreement seen on Rossmann is dataset\-dependent\. On datasets with high row vocabulary \(Berka, Fannie Mae, Freddie Mac, PTB\-XL\),NGP\(1\) already shows a wide spread among models, soNGP\(3\) refines rather than overturns the single\-token privacy conclusion\. On datasets with bounded row vocabulary \(Airbnb, Walmart\),NGP\(1\) saturates near the extremes andNGP\(3\) is the informative quantity\. Across all seven datasets, RTF retains the lowestNGP\(3\) on five datasets and is in the bottom two on the remaining two, confirming that autoregressive sequence\-level reproduction is an architecture\-level rather than a dataset\-specific effect\.

### E\.6\.Trajectory fidelity\.

Table 19\.TT\-Wasserstein distance after applyingInterpolation\-fill\. Lower values indicate better preservation of real\-data trajectory patterns\. The best synthetic result in each dataset is highlighted in bold\.TT\-Wasserstein distance results for Rossmann, Walmart, and PTB\-XL after applying Interpolation\-fill\. Rows correspond to the Original baseline and synthetic data generators, and columns correspond to datasets\. Lower values indicate better preservation of real\-data trajectory patterns\. The best synthetic result in each dataset is highlighted in bold\.MethodRossmannWalmartPTB\-XLOriginal0\.0320\.1360\.014ClavaDDPM0\.1110\.2030\.016RCTGAN0\.1360\.2330\.017RTF0\.0500\.2400\.018SDV0\.1360\.1820\.016RDBDiff0\.1360\.1970\.015RGCLD0\.0960\.2000\.016RelDiff0\.1380\.2640\.016TabDiT0\.045––Table[19](https://arxiv.org/html/2607.15606#A5.T19)reports TT\-Wasserstein distances across datasets and generators\. The Original column measures the distance between two real\-data splits and serves as a baseline for natural trajectory variation\. Synthetic datasets consistently exceed this baseline, indicating additional trajectory\-level discrepancies beyond inherent entity heterogeneity\. The best model varies by dataset, with TabDiT achieving the lowest distance on Rossmann, suggesting that explicit temporal modeling can help preserve trajectory\-level patterns\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/figs/rossmann_tabdit_ttw.png)Figure 7\.TT\-Wasserstein evaluation on the Rossmann dataset\. The upper panel shows raw trajectories, while the lower panel shows first\-differenced trajectories\.Figure[7](https://arxiv.org/html/2607.15606#A5.F7)shows that TT\-Wasserstein Distance is well aligned with visually observed trajectory fidelity\. Models with lower TTW, such as TabDiT and RTF, generate trajectories that more closely follow the real baseline in both raw values and first\-order differences\. In particular, TabDiT preserves not only the overall level and periodic trajectory shape, but also the timing and magnitude of abrupt changes, which explains its lowest distance\. By contrast, models with intermediate distances, such as RDBDIFF and ClavaDDPM, partially recover the timing of recurring fluctuations but underestimate or distort their transition magnitudes\. Models with larger distances produce trajectories that are either overly smoothed or structurally misaligned, indicating failure to preserve both global trajectory morphology and local temporal dynamics\.

Overall, the quantitative results show that model quality is highly metric\-dependent and cannot be fully characterized by static row\-level evaluation alone\. This highlights the importance of evaluating synthetic sequential tabular data across temporal, structural, privacy, and utility dimensions\. Full per\-metric results across all datasets are provided in Tables[21](https://arxiv.org/html/2607.15606#A5.T21)–[24](https://arxiv.org/html/2607.15606#A5.T24), while the SD metric results are reported in Table[20](https://arxiv.org/html/2607.15606#A5.T20)\.

### E\.7\.Qualitative Results

In this section, we provide qualitative analyses to complement the quantitative evaluation\. Although the proposed metrics summarize different aspects of fidelity, aggregate scores alone do not always reveal how these results manifest in individual examples\. We therefore present representative case studies to illustrate the qualitative behavior of synthetic data, including temporal patterns, visually apparent artifacts, and case\-specific failure modes\. These analyses help clarify where synthetic data successfully preserves the characteristics of real data and where it exhibits unrealistic or inconsistent behaviors that are difficult to interpret from numerical scores alone\.

#### E\.7\.1\.Synthetic data generation failure mode

##### Case 1: Duplicate timestamps and missing grid points\.

Figure[8](https://arxiv.org/html/2607.15606#A5.F8)shows a case in which the real trajectory fully covers the temporal grid, whereas the synthetic trajectory contains both duplicate timestamps and missing grid points\. Although the synthetic data are generated within the valid temporal range, their records are unevenly distributed across the temporal grid\. Several records are assigned to the same timestamp, while some grid positions observed in the real trajectory are not generated\. This indicates that the model captures the temporal support of the data but does not fully preserve the grid coverage structure\. The case illustrates that timestamp validity should be evaluated together with timestamp uniqueness and temporal grid coverage\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/figs/case_study_1.png)Figure 8\.Case study of duplicate timestamps and missing grid points\. Each point corresponds to one record, so the number of points at each timestamp represents the record count at that timestamp\. The real trajectory covers all timestamps without duplication, whereas the synthetic trajectory contains repeated timestamps and fails to cover several grid points\.
##### Case 2: Out\-of\-range timestamp generation\.

Figure[9](https://arxiv.org/html/2607.15606#A5.F9)presents a case in which the synthetic trajectory contains a timestamp outside the temporal support observed in the real data\. Although the synthetic trajectory has a comparable number of records to the real trajectory, one generated timestamp appears before the valid observation window\. This suggests that the model captures the overall event frequency to some extent, but does not fully preserve the temporal boundary of the data\. The case illustrates a discrepancy between sequence level plausibility and timestamp level validity, showing that a realistic trajectory length alone does not guarantee temporally valid synthetic records\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/figs/case_study_2.png)Figure 9\.Case study of out\-of\-range timestamp generation\. Each point corresponds to one record, so the number of points at each timestamp represents the record count at that timestamp\. The synthetic trajectory includes a timestamp outside the temporal support observed in the real data\.
##### Case 3: Temporal span truncation\.

Figure[10](https://arxiv.org/html/2607.15606#A5.F10)shows a case where the synthetic trajectory covers only a short subinterval of the real temporal support\. Although the generated timestamps are unique and remain within the valid range, the synthetic trajectory fails to reproduce the full temporal span of the real trajectory\. This failure mode is especially important because it may not appear as a boundary or duplication error, but still indicates poor preservation of trajectory duration and temporal coverage\.

![Refer to caption](https://arxiv.org/html/2607.15606v1/figs/case_study_3.png)Figure 10\.Case study of temporal span truncation\. Each point represents a generated record, and the number of points at each timestamp indicates the number of records assigned to that timestamp\. Generated data remain within the valid range but cover only part of the real temporal support\.Table 20\.Statistical\-distribution sub\-metric results across datasets and models\. Bold denotes the best score for each dataset–metric column, while underline denotes the second\-best score only when the best score is unique\.Statistical\-distribution sub\-metric table comparing synthetic data generators across datasets\. Rows correspond to dataset and model pairs, and columns report marginal distribution, correlation, support coverage, and contingency\-structure similarities\. Higher values indicate better fidelity\.DatasetModelKSComplementTVComplementStatisticSimilarityCorrelationSimilarityRangeCoverageCategoryCoverageContingencySimilarityStatisticMSASRossmannClavaDDPM0\.8120\.9010\.8240\.9460\.9980\.972\\mathbf\{0\.972\}0\.6620\.686RCTGAN0\.7550\.8380\.8260\.9560\.9960\.972\\mathbf\{0\.972\}0\.6050\.533RDBDiff0\.8100\.9050\.8230\.9480\.9980\.972\\mathbf\{0\.972\}0\.6600\.744RGCLD0\.7940\.9140\.8400\.9430\.9950\.8240\.4970\.762RelDiff0\.7700\.9080\.7690\.9500\.9870\.8610\.4920\.657SDV0\.7710\.6200\.8280\.9450\.9980\.6760\.3520\.685REaLTabFormer0\.7690\.8290\.7990\.9560\.9980\.8610\.5910\.669TabDiT0\.847\\mathbf\{0\.847\}0\.948\\mathbf\{0\.948\}0\.847\\mathbf\{0\.847\}0\.964\\mathbf\{0\.964\}1\.000\\mathbf\{1\.000\}0\.972\\mathbf\{0\.972\}0\.881\\mathbf\{0\.881\}1\.000\\mathbf\{1\.000\}BerkaClavaDDPM0\.9720\.9780\.9930\.9821\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9600\.701RCTGAN0\.8710\.8080\.9250\.9631\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.7270\.628RDBDiff0\.980\\mathbf\{0\.980\}0\.998\\mathbf\{0\.998\}0\.999\\mathbf\{0\.999\}0\.998\\mathbf\{0\.998\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.992\\mathbf\{0\.992\}0\.967\\mathbf\{0\.967\}RGCLD0\.9440\.8640\.9770\.9901\.000\\mathbf\{1\.000\}0\.9520\.7250\.924RelDiff0\.9330\.8640\.9570\.9821\.000\\mathbf\{1\.000\}0\.9540\.7240\.771SDV0\.6310\.6940\.6500\.9581\.000\\mathbf\{1\.000\}0\.8870\.4230\.322REaLTabFormer0\.9410\.9590\.9550\.9751\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9340\.846TabDiT0\.9570\.8160\.9700\.9811\.000\\mathbf\{1\.000\}0\.9540\.6740\.917AirbnbClavaDDPM0\.9620\.977\\mathbf\{0\.977\}0\.9680\.9901\.000\\mathbf\{1\.000\}0\.9790\.946\\mathbf\{0\.946\}0\.913\\mathbf\{0\.913\}RCTGAN0\.8780\.8620\.8940\.9581\.000\\mathbf\{1\.000\}0\.990\\mathbf\{0\.990\}0\.7980\.892RDBDiff0\.995\\mathbf\{0\.995\}0\.9390\.994\\mathbf\{0\.994\}0\.999\\mathbf\{0\.999\}1\.000\\mathbf\{1\.000\}0\.9890\.9390\.851RGCLD0\.9450\.9570\.9580\.9881\.000\\mathbf\{1\.000\}0\.8250\.9310\.795RelDiff0\.9350\.9290\.9340\.9731\.000\\mathbf\{1\.000\}0\.9480\.8710\.904SDV0\.8350\.3890\.9290\.9831\.000\\mathbf\{1\.000\}0\.6490\.2000\.702REaLTabFormer0\.8960\.8970\.8710\.9881\.000\\mathbf\{1\.000\}0\.9510\.8660\.559TabDiT0\.8880\.9430\.9490\.9791\.000\\mathbf\{1\.000\}0\.8090\.9140\.904Fannie MaeClavaDDPM0\.961\\mathbf\{0\.961\}0\.985\\mathbf\{0\.985\}0\.845\\mathbf\{0\.845\}0\.9830\.9730\.9670\.8330\.653RCTGAN0\.9190\.8820\.7610\.9740\.9710\.994\\mathbf\{0\.994\}0\.7620\.617RDBDiff0\.9160\.9490\.8040\.984\\mathbf\{0\.984\}0\.9740\.9390\.8100\.630RGCLD0\.9350\.9460\.7790\.9750\.9710\.9200\.8100\.910\\mathbf\{0\.910\}RelDiff0\.8880\.9680\.7530\.9770\.9640\.9840\.8120\.849SDV0\.6630\.8930\.7450\.9780\.976\\mathbf\{0\.976\}0\.8970\.7290\.630REaLTabFormer0\.7340\.9400\.7210\.9650\.8490\.9590\.894\\mathbf\{0\.894\}0\.767WalmartClavaDDPM0\.9360\.9290\.9730\.9840\.9960\.5830\.1380\.828RCTGAN0\.8080\.9210\.8780\.9281\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.7970\.560RDBDiff0\.963\\mathbf\{0\.963\}0\.9810\.989\\mathbf\{0\.989\}0\.990\\mathbf\{0\.990\}0\.9960\.5830\.1540\.864\\mathbf\{0\.864\}RGCLD0\.9290\.992\\mathbf\{0\.992\}0\.9760\.9850\.9970\.9960\.885\\mathbf\{0\.885\}0\.843RelDiff0\.9110\.9430\.9470\.9320\.9991\.000\\mathbf\{1\.000\}0\.8120\.643SDV0\.7960\.9270\.8120\.9541\.000\\mathbf\{1\.000\}0\.9880\.8070\.572REaLTabFormer0\.7390\.5860\.8620\.9120\.9820\.7920\.3040\.574Freddie MacClavaDDPM0\.9650\.9650\.984\\mathbf\{0\.984\}0\.9661\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9240\.743RCTGAN0\.8710\.9150\.9110\.9601\.000\\mathbf\{1\.000\}0\.9860\.8550\.556RDBDiff0\.989\\mathbf\{0\.989\}0\.999\\mathbf\{0\.999\}0\.9780\.999\\mathbf\{0\.999\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.968\\mathbf\{0\.968\}0\.956\\mathbf\{0\.956\}RGCLD0\.9800\.9710\.9770\.9961\.000\\mathbf\{1\.000\}0\.9790\.9400\.956\\mathbf\{0\.956\}RelDiff0\.8770\.9030\.8670\.9811\.000\\mathbf\{1\.000\}0\.9980\.8480\.882SDV0\.7150\.8070\.8700\.9831\.000\\mathbf\{1\.000\}0\.8540\.6090\.638REaLTabFormer0\.7450\.9460\.7750\.9550\.8980\.9460\.9530\.605PTB\-XLClavaDDPM0\.988\\mathbf\{0\.988\}0\.9460\.557\\mathbf\{0\.557\}0\.9941\.000\\mathbf\{1\.000\}0\.9230\.9050\.779RCTGAN0\.5990\.4600\.2980\.8981\.000\\mathbf\{1\.000\}0\.9020\.2260\.221RDBDiff0\.988\\mathbf\{0\.988\}0\.999\\mathbf\{0\.999\}0\.4430\.997\\mathbf\{0\.997\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.943\\mathbf\{0\.943\}0\.800\\mathbf\{0\.800\}RGCLD0\.9470\.6170\.2000\.9741\.000\\mathbf\{1\.000\}0\.6970\.3340\.767RelDiff0\.9680\.5840\.1790\.9111\.000\\mathbf\{1\.000\}0\.7240\.3260\.663SDV0\.8470\.7800\.3190\.9891\.000\\mathbf\{1\.000\}0\.8290\.5880\.710REaLTabFormer0\.8420\.6580\.1930\.9641\.000\\mathbf\{1\.000\}0\.5480\.0340\.757Citi BikeClavaDDPM0\.993\\mathbf\{0\.993\}0\.9710\.9730\.999\\mathbf\{0\.999\}0\.9971\.000\\mathbf\{1\.000\}0\.999\\mathbf\{0\.999\}–RCTGAN0\.9470\.8690\.9760\.9761\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.833–SDV0\.8960\.8700\.999\\mathbf\{0\.999\}0\.9931\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.424–CPAR0\.5120\.977\\mathbf\{0\.977\}0\.4850\.9540\.5001\.000\\mathbf\{1\.000\}0\.512–REaLTabFormer0\.7340\.9570\.6950\.9930\.7500\.9990\.964–TabularARGN0\.8110\.8880\.7580\.9680\.8750\.9560\.971–C\-MAPSSClavaDDPM0\.898–0\.987\\mathbf\{0\.987\}0\.999\\mathbf\{0\.999\}0\.969–––RCTGAN0\.709–0\.9050\.6361\.000\\mathbf\{1\.000\}–––SDV0\.758–0\.9640\.9421\.000\\mathbf\{1\.000\}–––CPAR0\.622–0\.987\\mathbf\{0\.987\}0\.6331\.000\\mathbf\{1\.000\}–––REaLTabFormer0\.918–0\.9740\.9951\.000\\mathbf\{1\.000\}–––TabularARGN0\.962\\mathbf\{0\.962\}–0\.9780\.9921\.000\\mathbf\{1\.000\}–––CouponClavaDDPM0\.8920\.8540\.8990\.9221\.000\\mathbf\{1\.000\}0\.9950\.7230\.877RCTGAN0\.8820\.8640\.9120\.9080\.9961\.000\\mathbf\{1\.000\}0\.7640\.826RDBDiff0\.984\\mathbf\{0\.984\}0\.981\\mathbf\{0\.981\}0\.987\\mathbf\{0\.987\}0\.979\\mathbf\{0\.979\}1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.957\\mathbf\{0\.957\}0\.919\\mathbf\{0\.919\}RGCLD0\.8630\.8660\.8670\.9210\.9881\.000\\mathbf\{1\.000\}0\.8060\.597RelDiff0\.8760\.7450\.9080\.9450\.9990\.9950\.6670\.916SDV0\.8730\.7150\.9200\.9191\.000\\mathbf\{1\.000\}0\.9640\.5440\.683Google ClusterClavaDDPM0\.9280\.7320\.8620\.9841\.000\\mathbf\{1\.000\}0\.8480\.879\\mathbf\{0\.879\}0\.673RCTGAN0\.7110\.5530\.7250\.9551\.000\\mathbf\{1\.000\}0\.8240\.4530\.500RDBDiff0\.946\\mathbf\{0\.946\}0\.938\\mathbf\{0\.938\}0\.974\\mathbf\{0\.974\}0\.996\\mathbf\{0\.996\}1\.000\\mathbf\{1\.000\}0\.952\\mathbf\{0\.952\}0\.8570\.814RGCLD0\.7550\.5200\.6200\.7650\.9960\.7400\.4350\.816RelDiff0\.8650\.6140\.6980\.9391\.000\\mathbf\{1\.000\}0\.7080\.6040\.823\\mathbf\{0\.823\}SDV0\.5040\.4970\.4830\.9410\.9950\.6130\.3310\.428H&MClavaDDPM0\.936\\mathbf\{0\.936\}0\.865\\mathbf\{0\.865\}0\.996\\mathbf\{0\.996\}0\.990\\mathbf\{0\.990\}1\.000\\mathbf\{1\.000\}0\.8930\.920\\mathbf\{0\.920\}0\.866RCTGAN0\.5310\.4300\.7720\.9821\.000\\mathbf\{1\.000\}0\.8750\.3350\.082RDBDiff0\.8820\.8140\.9130\.9751\.000\\mathbf\{1\.000\}0\.896\\mathbf\{0\.896\}0\.7640\.886RGCLD0\.9040\.8230\.9580\.9721\.000\\mathbf\{1\.000\}0\.7590\.7250\.828RelDiff0\.8270\.8000\.9510\.990\\mathbf\{0\.990\}1\.000\\mathbf\{1\.000\}0\.8030\.6700\.927\\mathbf\{0\.927\}SDV0\.5030\.6390\.6700\.9151\.000\\mathbf\{1\.000\}0\.8650\.4340\.103Home CreditClavaDDPM0\.4570\.6250\.3790\.8970\.9310\.8840\.4040\.791RCTGAN0\.7330\.8820\.7250\.9690\.9950\.9810\.7920\.724RDBDiff0\.740\\mathbf\{0\.740\}0\.909\\mathbf\{0\.909\}0\.925\\mathbf\{0\.925\}0\.995\\mathbf\{0\.995\}0\.9960\.985\\mathbf\{0\.985\}0\.823\\mathbf\{0\.823\}0\.795RGCLD0\.7290\.8350\.8010\.9850\.997\\mathbf\{0\.997\}0\.9240\.6950\.914\\mathbf\{0\.914\}RelDiff0\.7280\.8190\.6820\.9750\.997\\mathbf\{0\.997\}0\.9420\.6810\.787

Table 21\.Timestamp sub\-metric results across datasets and models\. Bold denotes the best score for each dataset–metric column, while underline denotes the second\-best score only when the best score is unique\.Timestamp sub\-metric table comparing synthetic data generators across datasets\. Rows correspond to dataset and model pairs, and columns report timestamp validity and temporal\-grid quality sub\-metrics\. Higher values indicate better fidelity\.DatasetModelTemporal OrderConsistencyTimestampUniquenessTrajectory DurationSimilarityTemporal RangeComplianceRegularityConsistencyGridCompletenessTime IntervalDistribution SimilarityRossmannClavaDDPM0\.5070\.6290\.4621\.000\\mathbf\{1\.000\}0\.4020\.644–RCTGAN0\.512\\mathbf\{0\.512\}0\.5940\.2870\.9970\.3720\.611–RDBDiff0\.5100\.6280\.4661\.000\\mathbf\{1\.000\}0\.4020\.644–RGCLD0\.5070\.6190\.4351\.000\\mathbf\{1\.000\}0\.3920\.636–RelDiff0\.5090\.6160\.5070\.9900\.3690\.618–SDV0\.5080\.5940\.3500\.9780\.3640\.596–REaLTabFormer0\.0010\.999\\mathbf\{0\.999\}0\.9421\.000\\mathbf\{1\.000\}0\.997\\mathbf\{0\.997\}0\.999\\mathbf\{0\.999\}–TabDiT0\.0230\.9781\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.9590\.983–BerkaClavaDDPM0\.5000\.914\\mathbf\{0\.914\}0\.0111\.000\\mathbf\{1\.000\}––0\.547RCTGAN0\.5030\.8940\.1160\.950––0\.637RDBDiff0\.5130\.5530\.944\\mathbf\{0\.944\}1\.000\\mathbf\{1\.000\}––0\.785RGCLD0\.5110\.6860\.5630\.988––0\.909RelDiff0\.5080\.8250\.0120\.915––0\.753SDV0\.5530\.3920\.2740\.989––0\.469REaLTabFormer0\.960\\mathbf\{0\.960\}0\.7160\.9130\.999––0\.947TabDiT0\.8650\.7410\.3330\.999––0\.949\\mathbf\{0\.949\}AirbnbClavaDDPM0\.5020\.9620\.947\\mathbf\{0\.947\}0\.981––0\.982\\mathbf\{0\.982\}RCTGAN0\.5100\.9000\.8800\.991––0\.921RDBDiff0\.5060\.978\\mathbf\{0\.978\}0\.8110\.951––0\.876RGCLD0\.5060\.9600\.7960\.986––0\.966RelDiff0\.5060\.9240\.9320\.996––0\.944SDV0\.541\\mathbf\{0\.541\}0\.8260\.9050\.949––0\.834REaLTabFormer0\.4970\.9720\.5610\.996––0\.861TabDiT0\.5020\.9530\.8840\.998\\mathbf\{0\.998\}––0\.963Fannie MaeClavaDDPM0\.5310\.6360\.773\\mathbf\{0\.773\}1\.000\\mathbf\{1\.000\}0\.235\\mathbf\{0\.235\}0\.225–RCTGAN0\.5090\.8910\.6350\.9500\.0110\.302–RDBDiff0\.5330\.6080\.5601\.000\\mathbf\{1\.000\}0\.2330\.492\\mathbf\{0\.492\}–RGCLD0\.535\\mathbf\{0\.535\}0\.6040\.6380\.9990\.2230\.021–RelDiff0\.5140\.8040\.7120\.9580\.1430\.458–SDV0\.4510\.9780\.0941\.000\\mathbf\{1\.000\}0\.0120\.352–REaLTabFormer0\.5110\.999\\mathbf\{0\.999\}0\.0530\.9780\.0260\.279–WalmartClavaDDPM0\.5940\.5780\.4221\.000\\mathbf\{1\.000\}0\.4060\.662–RCTGAN0\.4670\.939\\mathbf\{0\.939\}0\.2000\.8180\.0780\.658–RDBDiff0\.5890\.5780\.4001\.000\\mathbf\{1\.000\}0\.417\\mathbf\{0\.417\}0\.662–RGCLD0\.5500\.6670\.4001\.000\\mathbf\{1\.000\}0\.3110\.671–RelDiff0\.6110\.6220\.622\\mathbf\{0\.622\}1\.000\\mathbf\{1\.000\}0\.1390\.596–SDV0\.4830\.8560\.0001\.000\\mathbf\{1\.000\}0\.0610\.733\\mathbf\{0\.733\}–REaLTabFormer0\.662\\mathbf\{0\.662\}0\.3380\.0001\.000\\mathbf\{1\.000\}0\.3310\.400–Freddie MacClavaDDPM1\.000\\mathbf\{1\.000\}0\.6590\.7041\.000\\mathbf\{1\.000\}0\.2270\.691\\mathbf\{0\.691\}–RCTGAN1\.000\\mathbf\{1\.000\}0\.7570\.8360\.9710\.0270\.538–RDBDiff0\.5430\.6190\.9031\.000\\mathbf\{1\.000\}0\.242\\mathbf\{0\.242\}0\.653–RGCLD1\.000\\mathbf\{1\.000\}0\.6190\.9030\.9990\.2400\.654–RelDiff1\.000\\mathbf\{1\.000\}0\.6730\.918\\mathbf\{0\.918\}1\.000\\mathbf\{1\.000\}0\.2340\.688–SDV1\.000\\mathbf\{1\.000\}0\.9750\.8511\.000\\mathbf\{1\.000\}0\.0110\.644–REaLTabFormer0\.4850\.996\\mathbf\{0\.996\}0\.4560\.8500\.1030\.597–PTB\-XLClavaDDPM0\.5060\.6290\.4020\.9960\.4000\.633–RCTGAN0\.6240\.1120\.0760\.9910\.0550\.121–RDBDiff0\.5050\.6180\.3300\.9960\.3930\.622–RGCLD0\.5090\.5610\.2040\.9950\.3700\.565–RelDiff0\.5050\.6300\.3780\.9960\.4010\.633–SDV0\.5070\.5910\.9951\.000\\mathbf\{1\.000\}0\.3640\.596–REaLTabFormer1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.999\\mathbf\{0\.999\}1\.000\\mathbf\{1\.000\}0\.999\\mathbf\{0\.999\}0\.999\\mathbf\{0\.999\}–Citi BikeClavaDDPM0\.5001\.000\\mathbf\{1\.000\}0\.5891\.000\\mathbf\{1\.000\}––0\.759RCTGAN0\.5001\.000\\mathbf\{1\.000\}0\.6280\.995––0\.703SDV0\.5001\.000\\mathbf\{1\.000\}0\.727\\mathbf\{0\.727\}1\.000\\mathbf\{1\.000\}––0\.682CPAR0\.7891\.000\\mathbf\{1\.000\}0\.5830\.622––0\.612REaLTabFormer0\.5001\.000\\mathbf\{1\.000\}0\.0960\.883––0\.912\\mathbf\{0\.912\}TabularARGN0\.997\\mathbf\{0\.997\}0\.0030\.0020\.003––0\.000C\-MAPSSClavaDDPM0\.5020\.6480\.3070\.9960\.3520\.645–RCTGAN0\.7240\.0720\.3300\.9960\.0260\.069–SDV0\.5020\.6710\.0870\.9960\.3540\.660–CPAR1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}0\.836\\mathbf\{0\.836\}0\.9961\.000\\mathbf\{1\.000\}0\.981\\mathbf\{0\.981\}–REaLTabFormer0\.5010\.1250\.0641\.000\\mathbf\{1\.000\}0\.1230\.122–TabularARGN0\.5020\.6460\.3100\.9960\.3690\.647–CouponClavaDDPM0\.5010\.9670\.8591\.000\\mathbf\{1\.000\}––0\.815RCTGAN0\.5010\.979\\mathbf\{0\.979\}0\.8510\.961––0\.792RDBDiff0\.8190\.9680\.8811\.000\\mathbf\{1\.000\}––0\.810RGCLD0\.821\\mathbf\{0\.821\}0\.3060\.7400\.644––0\.517RelDiff0\.5120\.9600\.947\\mathbf\{0\.947\}1\.000\\mathbf\{1\.000\}––0\.822SDV0\.4960\.9460\.7501\.000\\mathbf\{1\.000\}––0\.833\\mathbf\{0\.833\}Google ClusterClavaDDPM0\.5650\.6740\.4520\.931––0\.398RCTGAN0\.5100\.8940\.2810\.886––0\.301RDBDiff0\.5660\.6670\.5500\.938\\mathbf\{0\.938\}––0\.412RGCLD0\.753\\mathbf\{0\.753\}0\.3970\.5660\.849––0\.683\\mathbf\{0\.683\}RelDiff0\.5970\.5950\.631\\mathbf\{0\.631\}0\.932––0\.468SDV0\.4840\.949\\mathbf\{0\.949\}0\.5230\.873––0\.319H&MClavaDDPM0\.5000\.928\\mathbf\{0\.928\}0\.6441\.000\\mathbf\{1\.000\}––0\.325RCTGAN0\.802\\mathbf\{0\.802\}0\.1180\.817\\mathbf\{0\.817\}0\.996––0\.813\\mathbf\{0\.813\}RDBDiff0\.5050\.9180\.6501\.000\\mathbf\{1\.000\}––0\.335RGCLD0\.5020\.9260\.7760\.985––0\.332RelDiff0\.5010\.9030\.6841\.000\\mathbf\{1\.000\}––0\.350SDV0\.7910\.0300\.3091\.000\\mathbf\{1\.000\}––0\.777Home CreditClavaDDPM0\.5050\.875\\mathbf\{0\.875\}0\.5611\.000\\mathbf\{1\.000\}0\.2930\.5020\.661RCTGAN0\.5130\.8070\.5981\.000\\mathbf\{1\.000\}0\.2890\.3540\.720RDBDiff0\.525\\mathbf\{0\.525\}0\.8060\.8021\.000\\mathbf\{1\.000\}0\.3590\.6360\.702RGCLD0\.5060\.8100\.950\\mathbf\{0\.950\}1\.000\\mathbf\{1\.000\}0\.399\\mathbf\{0\.399\}0\.655\\mathbf\{0\.655\}0\.714RelDiff0\.5050\.8730\.7171\.000\\mathbf\{1\.000\}0\.3070\.5460\.747\\mathbf\{0\.747\}

Table 22\.Cross\-sectional sub\-metric results across datasets and models\. Bold denotes the best score for each dataset–metric column, while underline denotes the second\-best score only when the best score is unique\.Cross\-sectional sub\-metric table comparing synthetic data generators across datasets\. Rows correspond to dataset and model pairs, and columns report distributional and dependency\-preservation sub\-metrics computed at each temporal slice\. Higher values indicate better fidelity\.DatasetModelCS KSComplementCS TVComplementCS StatisticSimilarityCS CorrelationSimilarityCS RangeCoverageCS CategoryCoverageCS ContingencySimilarityRossmannClavaDDPM0\.9510\.5470\.7750\.9600\.9900\.556\\mathbf\{0\.556\}0\.269RCTGAN0\.8740\.5430\.7230\.9610\.9290\.556\\mathbf\{0\.556\}0\.265RDBDiff0\.9480\.5480\.7740\.9610\.9900\.5550\.269RGCLD0\.9400\.5470\.7650\.9630\.9790\.556\\mathbf\{0\.556\}0\.268RelDiff0\.8810\.5460\.6810\.9570\.9230\.556\\mathbf\{0\.556\}0\.267SDV0\.5650\.0000\.7270\.9390\.7210\.0000\.000REaLTabFormer0\.9040\.5520\.8750\.9630\.9920\.556\\mathbf\{0\.556\}0\.275TabDiT0\.996\\mathbf\{0\.996\}0\.553\\mathbf\{0\.553\}0\.947\\mathbf\{0\.947\}0\.999\\mathbf\{0\.999\}1\.000\\mathbf\{1\.000\}0\.556\\mathbf\{0\.556\}0\.277\\mathbf\{0\.277\}BerkaClavaDDPM0\.5790\.6920\.8370\.8180\.7210\.7050\.474RCTGAN0\.5400\.5990\.8180\.8070\.7020\.6090\.370RDBDiff0\.742\\mathbf\{0\.742\}0\.829\\mathbf\{0\.829\}0\.923\\mathbf\{0\.923\}0\.880\\mathbf\{0\.880\}0\.894\\mathbf\{0\.894\}0\.810\\mathbf\{0\.810\}0\.723\\mathbf\{0\.723\}RGCLD0\.6720\.5990\.8710\.8240\.7880\.5620\.473RelDiff0\.6420\.5290\.8400\.8090\.7030\.5850\.362SDV0\.4290\.3880\.7200\.8550\.5340\.0640\.193REaLTabFormer0\.6090\.6440\.8180\.8090\.7170\.6300\.565TabDiT0\.6550\.5670\.8620\.8080\.7670\.5640\.442Fannie MaeClavaDDPM0\.993\\mathbf\{0\.993\}\-0\.0000\.868\\mathbf\{0\.868\}0\.997\\mathbf\{0\.997\}1\.000\\mathbf\{1\.000\}0\.000\-0\.000RCTGAN0\.895\-0\.0000\.4510\.9800\.9980\.000\-0\.000RDBDiff0\.9010\.0000\.4420\.9840\.9980\.000\-0\.000RGCLD0\.9520\.943\\mathbf\{0\.943\}0\.4760\.9770\.9990\.905\\mathbf\{0\.905\}0\.881\\mathbf\{0\.881\}RelDiff0\.8820\.0000\.2910\.9820\.9720\.0000\.000SDV0\.6460\.0000\.2740\.9830\.9940\.000\-0\.000REaLTabFormer0\.8280\.9220\.3920\.9780\.9570\.5050\.855WalmartClavaDDPM0\.8430\.4830\.5800\.9120\.968\\mathbf\{0\.968\}0\.5000\.000RCTGAN0\.7080\.9300\.4350\.8380\.8401\.000\\mathbf\{1\.000\}0\.864RDBDiff0\.852\\mathbf\{0\.852\}0\.4780\.604\\mathbf\{0\.604\}0\.921\\mathbf\{0\.921\}0\.9660\.5000\.000RGCLD0\.8360\.984\\mathbf\{0\.984\}0\.5740\.9170\.9661\.000\\mathbf\{1\.000\}0\.943\\mathbf\{0\.943\}RelDiff0\.7480\.9780\.4560\.8380\.8831\.000\\mathbf\{1\.000\}0\.923SDV0\.6320\.7060\.3990\.8890\.8500\.500–REaLTabFormer0\.6880\.7420\.4610\.8130\.8780\.3000\.493Freddie MacClavaDDPM0\.9720\.9590\.6790\.9631\.000\\mathbf\{1\.000\}0\.9900\.907RCTGAN0\.8550\.9050\.4180\.9510\.9850\.9760\.813RDBDiff0\.987\\mathbf\{0\.987\}0\.993\\mathbf\{0\.993\}0\.920\\mathbf\{0\.920\}0\.997\\mathbf\{0\.997\}1\.000\\mathbf\{1\.000\}0\.994\\mathbf\{0\.994\}0\.982\\mathbf\{0\.982\}RGCLD0\.9760\.9660\.6860\.9941\.000\\mathbf\{1\.000\}0\.9750\.912RelDiff0\.8690\.9010\.3660\.9800\.9960\.9930\.826SDV0\.6730\.8030\.2750\.9810\.9640\.8630\.623REaLTabFormer0\.8350\.9450\.4230\.9600\.9950\.3840\.900Citi BikeClavaDDPM0\.9570\.8800\.8950\.9910\.9960\.9640\.902RCTGAN0\.9060\.8060\.8370\.9701\.000\\mathbf\{1\.000\}0\.967\\mathbf\{0\.967\}0\.813SDV0\.9000\.7930\.8710\.9871\.000\\mathbf\{1\.000\}0\.967\\mathbf\{0\.967\}0\.415CPAR0\.4360\.8630\.2360\.9530\.3320\.967\\mathbf\{0\.967\}0\.509REaLTabFormer0\.968\\mathbf\{0\.968\}0\.921\\mathbf\{0\.921\}0\.950\\mathbf\{0\.950\}0\.992\\mathbf\{0\.992\}0\.9990\.4160\.946\\mathbf\{0\.946\}TabularARGN0\.8530\.5350\.7580\.9300\.9990\.3960\.829CouponClavaDDPM0\.753\\mathbf\{0\.753\}0\.743\\mathbf\{0\.743\}0\.832\\mathbf\{0\.832\}0\.9080\.9680\.8780\.528\\mathbf\{0\.528\}RCTGAN0\.7510\.7370\.8220\.9080\.9650\.881\\mathbf\{0\.881\}0\.523RDBDiff0\.7490\.7170\.8110\.909\\mathbf\{0\.909\}0\.972\\mathbf\{0\.972\}0\.8700\.498RGCLD0\.7050\.6750\.7830\.8790\.9650\.7160\.436RelDiff0\.7400\.6950\.8070\.9050\.9670\.8620\.476SDV0\.4100\.4100\.5140\.5620\.9600\.3200\.143H&MClavaDDPM0\.871\\mathbf\{0\.871\}0\.766\\mathbf\{0\.766\}0\.824\\mathbf\{0\.824\}0\.9680\.998\\mathbf\{0\.998\}0\.740\\mathbf\{0\.740\}0\.571\\mathbf\{0\.571\}RCTGAN0\.5890\.3570\.3710\.8730\.9640\.3590\.137RDBDiff0\.8080\.7320\.4850\.9690\.9520\.6710\.513RGCLD0\.8490\.7540\.8030\.9660\.998\\mathbf\{0\.998\}0\.6970\.547RelDiff0\.8100\.7250\.7160\.9670\.9930\.6990\.510SDV0\.3130\.3420\.1570\.978\\mathbf\{0\.978\}0\.4930\.0030\.141

Table 23\.Longitudinal sub\-metric results across datasets and models\. TT\-Wasserstein is computed as1−TT​\-​W1\-\\mathrm\{TT\\text\{\-\}W\}so that higher values indicate better fidelity; it is reported only for Rossmann, Walmart, and PTB\-XL\. Bold denotes the best score for each dataset–metric column, while underline denotes the second\-best score only when the best score is unique\.Longitudinal sub\-metric table comparing synthetic data generators across datasets\. Rows correspond to dataset and model pairs, and columns report trajectory\-level dynamic similarity metrics\. TT\-Wasserstein is reported as one minus the original TT\-W distance and is shown only for Rossmann, Walmart, and PTB\-XL; inapplicable datasets are marked with dashes\.DatasetModelFirst DifferenceKS ComplementTransition MatrixTV ComplementAutoCorrelationSimilarityTT\-WassersteinRossmannClavaDDPM0\.9750\.9580\.9280\.905RCTGAN0\.9710\.9180\.8720\.880RDBDiff0\.9450\.9540\.9260\.921RGCLD0\.9600\.9470\.9240\.899RelDiff0\.9660\.9200\.8980\.880SDV0\.9000\.8680\.6750\.880REaLTabFormer0\.9780\.981\\mathbf\{0\.981\}0\.9410\.946TabDiT0\.998\\mathbf\{0\.998\}0\.9800\.954\\mathbf\{0\.954\}0\.991\\mathbf\{0\.991\}BerkaClavaDDPM0\.9410\.8290\.860–RCTGAN0\.9370\.8060\.832–RDBDiff0\.9560\.913\\mathbf\{0\.913\}0\.980\\mathbf\{0\.980\}–RGCLD0\.9450\.8230\.884–RelDiff0\.9360\.8150\.852–SDV0\.4820\.5720\.925–REaLTabFormer0\.9650\.8450\.877–TabDiT0\.969\\mathbf\{0\.969\}0\.8270\.871–AirbnbClavaDDPM1\.000\\mathbf\{1\.000\}0\.9080\.995–RCTGAN1\.000\\mathbf\{1\.000\}0\.9090\.995–RDBDiff1\.000\\mathbf\{1\.000\}0\.9000\.996\\mathbf\{0\.996\}–RGCLD1\.000\\mathbf\{1\.000\}0\.9100\.994–RelDiff1\.000\\mathbf\{1\.000\}0\.9080\.996\\mathbf\{0\.996\}–SDV–0\.939\\mathbf\{0\.939\}––REaLTabFormer1\.000\\mathbf\{1\.000\}0\.8990\.994–TabDiT1\.000\\mathbf\{1\.000\}0\.9030\.994–Fannie MaeClavaDDPM0\.6220\.7960\.980\\mathbf\{0\.980\}–RCTGAN0\.6080\.7860\.914–RDBDiff0\.6270\.7970\.857–RGCLD0\.7470\.863\\mathbf\{0\.863\}0\.891–RelDiff0\.6460\.8120\.909–SDV0\.7380\.8040\.932–REaLTabFormer0\.789\\mathbf\{0\.789\}0\.8380\.693–WalmartClavaDDPM0\.8830\.9220\.938\\mathbf\{0\.938\}0\.783RCTGAN0\.8620\.9000\.8370\.772RDBDiff0\.8730\.9210\.8600\.792RGCLD0\.891\\mathbf\{0\.891\}0\.927\\mathbf\{0\.927\}0\.8530\.797\\mathbf\{0\.797\}RelDiff0\.8760\.9180\.7980\.786SDV0\.8600\.6100\.8000\.796REaLTabFormer0\.8520\.7440\.4370\.729Freddie MacClavaDDPM0\.5840\.849\\mathbf\{0\.849\}0\.971–RCTGAN0\.5440\.8320\.900–RDBDiff0\.791\\mathbf\{0\.791\}0\.8380\.977\\mathbf\{0\.977\}–RGCLD0\.7160\.8350\.939–RelDiff0\.6510\.849\\mathbf\{0\.849\}0\.905–SDV0\.5650\.7790\.840–REaLTabFormer0\.6970\.4860\.712–PTB\-XLClavaDDPM0\.9670\.7370\.8480\.965\\mathbf\{0\.965\}RCTGAN0\.7650\.7470\.8080\.951RDBDiff0\.9180\.7710\.8420\.965\\mathbf\{0\.965\}RGCLD0\.9340\.7720\.8190\.965\\mathbf\{0\.965\}RelDiff0\.9680\.7630\.8360\.961SDV0\.9460\.971\\mathbf\{0\.971\}0\.850\\mathbf\{0\.850\}0\.963REaLTabFormer0\.982\\mathbf\{0\.982\}0\.7740\.7980\.965\\mathbf\{0\.965\}Citi BikeClavaDDPM0\.935–0\.995–RCTGAN0\.928–0\.992–SDV0\.906–0\.994–CPAR0\.628–0\.994–REaLTabFormer0\.937\\mathbf\{0\.937\}–0\.997\\mathbf\{0\.997\}–TabularARGN0\.876–0\.966–C\-MAPSSClavaDDPM0\.897–0\.902–RCTGAN0\.760–0\.907–SDV0\.859–0\.924\\mathbf\{0\.924\}–CPAR0\.809–0\.893–REaLTabFormer0\.973\\mathbf\{0\.973\}–0\.853–TabularARGN0\.897–0\.780–CouponClavaDDPM0\.8890\.8520\.787–RCTGAN0\.8790\.8530\.755–RDBDiff0\.8740\.8450\.933\\mathbf\{0\.933\}–RGCLD0\.935\\mathbf\{0\.935\}0\.891\\mathbf\{0\.891\}0\.847–RelDiff0\.9270\.8650\.932–SDV0\.8060\.8800\.825–Google ClusterClavaDDPM0\.721–0\.789–RCTGAN0\.620–0\.795–RDBDiff0\.801–0\.786–RGCLD0\.802\\mathbf\{0\.802\}–0\.797–RelDiff0\.668–0\.775–SDV0\.661–0\.823\\mathbf\{0\.823\}–H&MClavaDDPM0\.8930\.822\\mathbf\{0\.822\}0\.966–RCTGAN0\.7820\.5650\.598–RDBDiff0\.9110\.6800\.590–RGCLD0\.925\\mathbf\{0\.925\}0\.8090\.975\\mathbf\{0\.975\}–RelDiff0\.8910\.7590\.694–SDV0\.778–0\.582–Home CreditClavaDDPM0\.9400\.8950\.935–RCTGAN0\.8810\.8440\.899–RDBDiff0\.9390\.8820\.945–RGCLD0\.958\\mathbf\{0\.958\}0\.900\\mathbf\{0\.900\}0\.949\\mathbf\{0\.949\}–RelDiff0\.9350\.8830\.898–

Table 24\.Structural sub\-metric results across datasets and models\. Bold denotes the best score for each dataset–metric column, while underline denotes the second\-best score only when the best score is unique\.Structural sub\-metric table comparing synthetic data generators across datasets\. Rows correspond to dataset and model pairs, and columns report sequence\-length, cardinality\-shape, and dynamic relational\-structure similarities\. Higher values indicate better fidelity\.DatasetModelSequence LengthSimilarityTemporal CardinalityShape SimilarityDynamic K\-HopCorrelation SimilarityRossmannClavaDDPM1\.000\\mathbf\{1\.000\}––RCTGAN1\.000\\mathbf\{1\.000\}––RDBDiff1\.000\\mathbf\{1\.000\}––RGCLD1\.000\\mathbf\{1\.000\}––RelDiff1\.000\\mathbf\{1\.000\}––SDV1\.000\\mathbf\{1\.000\}––REaLTabFormer1\.000\\mathbf\{1\.000\}––TabDiT1\.000\\mathbf\{1\.000\}––BerkaClavaDDPM0\.993––RCTGAN0\.952––RDBDiff1\.000\\mathbf\{1\.000\}––RGCLD0\.993––RelDiff1\.000\\mathbf\{1\.000\}––SDV0\.814––REaLTabFormer0\.952––TabDiT0\.958––AirbnbClavaDDPM0\.987––RCTGAN0\.924––RDBDiff1\.000\\mathbf\{1\.000\}––RGCLD0\.981––RelDiff1\.000\\mathbf\{1\.000\}––SDV0\.938––REaLTabFormer0\.631––TabDiT0\.912––Fannie MaeClavaDDPM0\.998\\mathbf\{0\.998\}––RCTGAN0\.953––RDBDiff0\.822––RGCLD0\.990––RelDiff0\.750––SDV0\.848––REaLTabFormer0\.817––WalmartClavaDDPM0\.9560\.7040\.931RCTGAN0\.8440\.5470\.801RDBDiff1\.000\\mathbf\{1\.000\}0\.7090\.953\\mathbf\{0\.953\}RGCLD0\.9670\.729\\mathbf\{0\.729\}0\.950RelDiff1\.000\\mathbf\{1\.000\}0\.5910\.822SDV0\.8780\.5980\.881REaLTabFormer0\.3220\.4200\.811Freddie MacClavaDDPM0\.995––RCTGAN0\.972––RDBDiff1\.000\\mathbf\{1\.000\}––RGCLD0\.993––RelDiff1\.000\\mathbf\{1\.000\}––SDV0\.965––REaLTabFormer0\.695––PTB\-XLClavaDDPM1\.000\\mathbf\{1\.000\}––RCTGAN1\.000\\mathbf\{1\.000\}––RDBDiff1\.000\\mathbf\{1\.000\}––RGCLD1\.000\\mathbf\{1\.000\}––RelDiff1\.000\\mathbf\{1\.000\}––SDV1\.000\\mathbf\{1\.000\}––REaLTabFormer0\.999––Citi BikeClavaDDPM0\.908––RCTGAN0\.979\\mathbf\{0\.979\}––SDV0\.979\\mathbf\{0\.979\}––CPAR0\.271––REaLTabFormer0\.676––TabularARGN0\.154––C\-MAPSSClavaDDPM0\.709––RCTGAN0\.330––SDV0\.961\\mathbf\{0\.961\}––CPAR0\.836––REaLTabFormer0\.000––TabularARGN0\.917––CouponClavaDDPM0\.9900\.9980\.917RCTGAN0\.8340\.9980\.898RDBDiff1\.000\\mathbf\{1\.000\}0\.999\\mathbf\{0\.999\}0\.956\\mathbf\{0\.956\}RGCLD1\.000\\mathbf\{1\.000\}0\.9950\.920RelDiff1\.000\\mathbf\{1\.000\}0\.999\\mathbf\{0\.999\}0\.927SDV0\.6690\.999\\mathbf\{0\.999\}0\.921Google ClusterClavaDDPM0\.9700\.984–RCTGAN0\.6910\.725–RDBDiff1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}–RGCLD0\.9810\.991–RelDiff1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}–SDV0\.4770\.656–H&MClavaDDPM0\.640––RCTGAN0\.555––RDBDiff0\.638––RGCLD0\.640––RelDiff0\.640––SDV0\.648\\mathbf\{0\.648\}––Home CreditClavaDDPM0\.9650\.940–RCTGAN0\.8420\.898–RDBDiff0\.9950\.998–RGCLD0\.9910\.997–RelDiff1\.000\\mathbf\{1\.000\}1\.000\\mathbf\{1\.000\}–