Represent, Then Generate: Multimodal-Conditioned Time-Series Generation under Irregular Missingness

# 1Introduction
Source: [https://arxiv.org/html/2608.12592](https://arxiv.org/html/2608.12592)
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Represent, Then Generate: Multimodal\-Conditioned Time\-Series Generation under Irregular MissingnessHaochen Zhang1\{\}^\{\\,1\\,\},Jiaheng Guo1\{\}^\{\\,1\\,\},Yu\-Chao Huang1\{\}^\{\\,1\\,\},Nicholas Konz1\{\}^\{\\,1\\,\}andTianlong Chen1​🖂\{\}^\{\\,1\\,\\textrm\{\\Letter\}\}1\{\}^\{1\\,\}UNITES Lab, University of North Carolina at Chapel Hill\{haochenz,morris,nick124, tianlong\}@cs\.unc\.edu, jiaheng@unc\.edu🖂\{\}^\{\\textrm\{\\Letter\}\}Corresponding AuthorContinuous physiological time series underpin modern clinical monitoring, yet many of the most informative signals are invasive, expensive, or simply unavailable for a given patient\. Conditional generation offers a remedy: an absent signal can be synthesized from co\-recorded signals and routine clinical variables\. Existing generators, however, are built around a single conditioning modality and degrade when forced to handle the heterogeneous, irregularly missing mix of time\-variant signals and static covariates seen in practice\. We propose ReCoGen \(RepresentConditions, thenGenerate\), a two\-stage framework that decouples multimodal condition representation from target generation\. Stage I trains one masked autoencoder per modality, distilling each time\-variant condition into a compact and missingness\-tolerant token sequence\. Stage II trains a flow\-matching generator that fuses these tokens with static conditions to synthesize the target signal\. Across three physiological benchmarks, including continuous glucose monitoring on AI\-READI and arterial blood pressure generation on MIMIC\-III and MIMIC\-IV, ReCoGen attains the best downstream utility on all sixteen \(dataset, task, metric\) settings, surpassing six representative conditional generators; on thirteen of them its utility also reaches or exceeds the utility measured on the real signal, a reference we read as an approximate anchor rather than a ceiling\. Ablations trace the gains to the conditioning path: learnable cross\-attention over the frozen per\-modality encoders, and a dual token\-plus\-AdaLN route for the static conditions\. ReCoGen thus turns routinely collected signals into informative surrogates for invasive or unavailable ones, a step toward less invasive, lower\-cost continuous clinical monitoring\.

00footnotetext:🖂\{\}^\{\\textrm\{\\Letter\}\}Corresponding authors: \{tianlong\}@cs\.unc\.edu
Preprint\. Under review\.### 1Introduction

Continuous physiological time series have become a foundation of modern medicine\([35](https://arxiv.org/html/2608.12592#bib.bib28);[6](https://arxiv.org/html/2608.12592#bib.bib29)\): bedside monitors and consumer wearables now collect cardiac, respiratory, and metabolic signals that trace a patient’s health state and support diagnosis, risk stratification, and the early warning of adverse events\. Intensive\-care vital\-sign streams support prediction of in\-hospital mortality\([10](https://arxiv.org/html/2608.12592#bib.bib1);[3](https://arxiv.org/html/2608.12592#bib.bib9)\), early sepsis onset\([29](https://arxiv.org/html/2608.12592#bib.bib6)\), and impending circulatory failure\([13](https://arxiv.org/html/2608.12592#bib.bib2)\); wearable continuous glucose monitoring enables more precise screening for diabetes\([9](https://arxiv.org/html/2608.12592#bib.bib4);[25](https://arxiv.org/html/2608.12592#bib.bib5)\)\.

However, many informative signals are difficult and costly to obtain\. Continuous arterial blood pressure \(ABP\) acquisition is invasive and carries procedural risk, so it is used for only a minority of patients\([30](https://arxiv.org/html/2608.12592#bib.bib30)\); and signals that are easy to collect often arrive with irregular missingness, which materially complicates downstream use\([5](https://arxiv.org/html/2608.12592#bib.bib31)\)\. Conditional time series generation is a remedy: synthesize the hard\-to\-measure target from available co\-recorded modalities, as in cross\-modal biosignal synthesis\([32](https://arxiv.org/html/2608.12592#bib.bib16)\)and generative augmentation of physiological recordings\([22](https://arxiv.org/html/2608.12592#bib.bib10)\), so that monitoring and analysis extend to settings where the target is unavailable or hard to access\([17](https://arxiv.org/html/2608.12592#bib.bib15)\)\.

![Refer to caption](https://arxiv.org/html/2608.12592v1/Figures/figure0.png)Figure 1:Motivation and overview\. \(A\) Existing conditional generators ingest multimodal physiological conditions directly and fail on heterogeneous modalities with irregular missingness\. \(B\) ReCoGen first represents each condition modality with missingness\-aware encoders, then generates the target with a conditional flow\-matching model\.Conditional time series generation methods have been studied for handling a wide range of conditioning signals\([28](https://arxiv.org/html/2608.12592#bib.bib11)\)\. Label\-conditioned methods synthesize time series from discrete class labels\([22](https://arxiv.org/html/2608.12592#bib.bib10);[19](https://arxiv.org/html/2608.12592#bib.bib12)\)\. Attribute\-conditioned methods condition on structured metadata\([14](https://arxiv.org/html/2608.12592#bib.bib13);[33](https://arxiv.org/html/2608.12592#bib.bib14)\)\. Text\-conditioned models convert the conditions into natural language description to enable flexibly controllable generation\([8](https://arxiv.org/html/2608.12592#bib.bib17);[20](https://arxiv.org/html/2608.12592#bib.bib19);[17](https://arxiv.org/html/2608.12592#bib.bib15)\)\. Imputation methods infill the missing part conditioned on the observed proportion of a multivariate time series\([34](https://arxiv.org/html/2608.12592#bib.bib20);[37](https://arxiv.org/html/2608.12592#bib.bib21);[27](https://arxiv.org/html/2608.12592#bib.bib22)\)\. However, these methods are mainly built for a single conditioning modality, whereas clinical conditioning signals are inevitably multimodal: the target must be generated jointly from several co\-recorded time series together with static tabular and categorical clinical variables\. Even methods designed for heterogeneous covariates\([28](https://arxiv.org/html/2608.12592#bib.bib11)\)do not address irregularly sampled covariates or modality missingness, which characterize wearable and ICU data\([5](https://arxiv.org/html/2608.12592#bib.bib31)\)\. Representing and merging conditions across modalities to build a robust conditional generator remains an open problem\.

The most straightforward way to build such a system from existing methods is to fold the conditions from multiple modalities directly into the generator: treating every co\-recorded time series as observed context, as in imputation methods\([34](https://arxiv.org/html/2608.12592#bib.bib20);[37](https://arxiv.org/html/2608.12592#bib.bib21);[27](https://arxiv.org/html/2608.12592#bib.bib22)\), and handling the static conditions with attribute\-conditioned methods\([28](https://arxiv.org/html/2608.12592#bib.bib11)\)\. Multimodal physiological conditions are precisely where this shortcut breaks down \(Figure[1](https://arxiv.org/html/2608.12592#S1.F1)A\), for two reasons\. First, co\-recorded time series arise from distinct physiological processes with their own dynamics and clinical meaning\([4](https://arxiv.org/html/2608.12592#bib.bib32);[1](https://arxiv.org/html/2608.12592#bib.bib33)\), so an in\-painting mechanism that treats them as homogeneous context cannot represent these modality\-specific semantics\. Second, each modality has its own irregular sampling grid and missingness pattern, making it hard to learn representations of the time\-variant conditions while performing generation\. Indeed, handing the raw, partially observed streams straight to the generator measurably degrades the synthesized target on the harder downstream tasks \(Figure[4](https://arxiv.org/html/2608.12592#S3.F4)\)\. This leads us to a simple hypothesis: properly representing a condition deserves as much attention as generating the target\.

We validate this hypothesis and propose ReCoGen: a two\-stage framework for multimodal\-conditioned physiological time\-series generation that decouples condition representation from target generation \(Figure[1](https://arxiv.org/html/2608.12592#S1.F1)B\)\. In Stage I we learn one masked autoencoder per modality\([12](https://arxiv.org/html/2608.12592#bib.bib34)\), so each encoder imputes from context and distills an irregular, time\-variant modality into a compact, robust token sequence\. In Stage II we freeze these encoders and train a flow\-matching model\([23](https://arxiv.org/html/2608.12592#bib.bib35);[24](https://arxiv.org/html/2608.12592#bib.bib36)\)that synthesizes the target from both static and time\-variant conditions, where we find the conditioning\-path design has a substantial effect on downstream utility\. Our contributions are as follows:

- •We show that the current methods for conditional time\-series generation perform poorly under multimodal physiological conditioning; and we trace the failure to the absence of a dedicated, missingness\-aware condition representation\.
- •We propose ReCoGen, a two\-stage framework that decouples condition representation from generation: per\-modality masked autoencoders distill each irregular modality into missingness\-tolerant tokens; and the conditional generator can merge conditioning features in a separate training stage\.
- •We conduct comprehensive experiments across three physiological datasets, showing that ReCoGen outperforms six representative conditional generators in downstream task utility; through a systematic ablation study, we explain the intuition behind the design of ReCoGen\.

### 2Method

#### 2\.1Problem Setup

We study the generation of a physiological time series from the other signals and clinical variables recorded for the same subject\. The targetXXis valued inℝV×T\\mathbb\{R\}^\{V\\times T\}\(VVchannels of lengthTT\)\. The conditions come in two forms:MMco\-recorded time\-variant modalities, themm\-th valued inℝTm\\mathbb\{R\}^\{T\_\{m\}\}and possibly irregularly sampled, each paired with a binary observed masko\(m\)∈\{0,1\}Tmo^\{\(m\)\}\\in\\\{0,1\\\}^\{T\_\{m\}\}\(11at observed steps,00at missing ones\); and a static descriptorssin an abstract space𝒮\\mathcal\{S\}— questionnaire responses, laboratory tests, or medical history, varying across cohorts\. Writingc=\(c\(1\),o\(1\),…,c\(M\),o\(M\),s\)c=\(c^\{\(1\)\},o^\{\(1\)\},\\dots,c^\{\(M\)\},o^\{\(M\)\},s\)for a realization of the joint conditionCC, the goal is to learnP^θ​\(X∣C\)≈P⁡\(X∣C\)\\widehat\{P\}\_\{\\theta\}\(X\\mid C\)\\approx P\(X\\mid C\)from i\.i\.d\. samples\{\(xi,ci\)\}i=1N\\\{\(x\_\{i\},c\_\{i\}\)\\\}\_\{i=1\}^\{N\}of the unknown joint distributionPP\.

We take a data\-augmentation view of generation quality: generated signals should be as useful as real ones for a downstream clinical predictor\. Fix a label space𝒴\\mathcal\{Y\}, a hypothesis classℋ\\mathcal\{H\}of predictorsh:ℝV×T→𝒴h:\\mathbb\{R\}^\{V\\times T\}\\\!\\to\\mathcal\{Y\}and a lossLL; writeRQ​\(h\)=𝔼\(x,ℓ\)∼Q​\[L⁡\(h⁡\(x\),ℓ\)\]R\_\{Q\}\(h\)=\\mathbb\{E\}\_\{\(x,\\ell\)\\sim Q\}\[L\(h\(x\),\\ell\)\]for the risk under a distributionQQover signal–label pairs, and leth⋆=arg⁡minh∈ℋ​RP​\(h\)h^\{\\star\}=\\arg\\min\_\{h\\in\\mathcal\{H\}\}R\_\{P\}\(h\)be the predictor a practitioner would train on real data\. Our generator induces a synthetic distributionP^θ\\widehat\{P\}\_\{\\theta\}, under which a signal is generated from the real conditions and paired with the same label\. Generation serves augmentation well when the generalization gap

Δ\(θ\)=𝔼\(c,ℓ\)𝔼x^∼P^θ\(⋅∣c\)\[L\(h⋆\(x^\),ℓ\)\]−RP\(h⋆\)\\Delta\(\\theta\)=\\mathbb\{E\}\_\{\(c,\\ell\)\}\\mathbb\{E\}\_\{\\widehat\{x\}\\sim\\widehat\{P\}\_\{\\theta\}\(\\cdot\\mid c\)\}\\big\[L\(h^\{\\star\}\(\\widehat\{x\}\),\\ell\)\\big\]\-R\_\{P\}\(h^\{\\star\}\)\(2\.1\)is small in magnitude; we estimate both risks on held\-out subjects and report them as AUROC and AUPRC, for which a lower risk is a higher value\. Three qualifications fix howΔ⁡\(θ\)\\Delta\(\\theta\)should be read: the quantity to control is\|Δ⁡\(θ\)\|\|\\Delta\(\\theta\)\|, since the gap is signed and a large negative gap is not better than a zero gap; it is informative only whenRP​\(h⋆\)R\_\{P\}\(h^\{\\star\}\)is itself non\-trivial, as otherwise both risks sit near the floor and their agreement certifies nothing; and it is necessary but not sufficient for fidelity, since a generator preserving only the label\-relevant component ofxxalso attainsΔ⁡\(θ\)≈0\\Delta\(\\theta\)\\approx 0\. In particularΔ⁡\(θ\)<0\\Delta\(\\theta\)<0calls for scrutiny rather than celebration: it is the signature one would expect if the generator re\-expressed the conditions in a form the predictor reads more easily than the measured waveform, a point we return to with the main results\.

#### 2\.2Overview of ReCoGen

![Refer to caption](https://arxiv.org/html/2608.12592v1/figure1.png)Figure 2:Overview of ReCoGen\. Stage I trains one masked autoencoder per time\-variant conditioning modality; Stage II freezes them and trains a conditional flow\-matching generator fusing the time\-variant and static conditions to synthesize the target series\.ReCoGen generates a target from its conditions in two decoupled stages \(Figure[2](https://arxiv.org/html/2608.12592#S2.F2)\)\. For each irregular time\-variant modality, Stage I learns a robust encoder by training a lightweight Transformer encoder–decoder over the full\-length event stream under a masked\-reconstruction objective that forces the encoder to impute from context\. Stage II freezes those encoders and trains a conditional flow\-matching generator that combines the time\-variant and the static conditions to synthesize the target series\. Both stages operate in the observation domain: the generator represents a 1\-D series as a 2\-D image through an invertible delay embedding\([27](https://arxiv.org/html/2608.12592#bib.bib22)\)and models it with a vision transformer\.

ReCoGen rests on two core designs\. The first is the decoupled training just outlined: the feature extractor for the time\-variant conditions is trained on its own masked\-reconstruction objective and then frozen, so the generator is optimized on top of fixed conditioning features instead of having to learn how to encode irregular, partially observed series jointly with generation\. The second is the conditioning path\. Each time\-variant modality is summarized by a bank of learnable per\-modality query tokens that cross\-attend over its frozen autoencoder latents, giving a compact set of in\-context condition tokens; the static descriptor enters through two complementary routes, as an additional in\-context token and as an adaptive layer\-norm \(AdaLN\) modulation\. This path accounts for most of the generation quality\.

#### 2\.3Stage I: Masked Autoencoder Training

We learn the representation of each time\-variant conditioning modality with a masked autoencoder\. Take one modality and write its series asu=\(u1,…,uL\)u=\(u\_\{1\},\\dots,u\_\{L\}\)with observed masko∈\{0,1\}Lo\\in\\\{0,1\\\}^\{L\}\(a genericc\(m\)c^\{\(m\)\}ando\(m\)o^\{\(m\)\}\), whereot=1o\_\{t\}=1marks a genuinely observed step andot=0o\_\{t\}=0a step that is missing\. The observed steps𝒪=\{t:ot=1\}\\mathcal\{O\}=\\\{t:o\_\{t\}=1\\\}already leave a modality\-dependent fraction of the series missing; on top of this natural missingness we sample a random subsetℳ⊆𝒪\\mathcal\{M\}\\subseteq\\mathcal\{O\}with mask ratioρ\\rhoand hold it out for reconstruction\. Every naturally missing or held\-out step is replaced by a single shared learnable \[missing\] token, so the encoder always sees a regular\-length sequence\. Following masked autoencoding\([12](https://arxiv.org/html/2608.12592#bib.bib34)\), the loss is the mean squared error on the held\-out steps only,

ℒAE=1\|ℳ\|​∑t∈ℳ\(u^t−ut\)2\.\\mathcal\{L\}\_\{\\mathrm\{AE\}\}=\\frac\{1\}\{\|\\mathcal\{M\}\|\}\\sum\_\{t\\in\\mathcal\{M\}\}\\big\(\\widehat\{u\}\_\{t\}\-u\_\{t\}\\big\)^\{2\}\.\(2\.2\)Reconstructing unseen points forces the encoder to infer from context rather than copy its input, which keeps it robust when a modality is sparsely observed\. We train one autoencoderAEm\\mathrm\{AE\}\_\{m\}per modalitymm, freeze it for Stage II, and useρ=0\.3\\rho\{=\}0\.3by default\.

#### 2\.4Stage II: Conditional Flow\-Matching Training

Stage II trains a conditional generator on top of the frozen Stage I encoders, which now act as fixed feature extractors; on the conditioning side only the injection modules remain trainable, which also stabilizes training\. A time seriesx∈ℝV×Tx\\in\\mathbb\{R\}^\{V\\times T\}is mapped to a square imageΦ=𝒟⁡\(x\)∈ℝV×e×e\\Phi=\\mathcal\{D\}\(x\)\\in\\mathbb\{R\}^\{V\\times e\\times e\}by a delay embedding\([27](https://arxiv.org/html/2608.12592#bib.bib22)\), whoseii\-th column is the non\-overlapping length\-eewindowx\[ie:\(i\+1\)e\]x\[\\,ie:\(i\{\+\}1\)e\\,\]\(embedding dimensionee\), padded to ane×ee\\times esquare\. The map𝒟\\mathcal\{D\}is invertible on the valid region, so a generated image is read back to a series by𝒟−1\\mathcal\{D\}^\{\-1\}, and a binary maskΦmask\\Phi\_\{\\text\{mask\}\}marks the non\-padded pixels, on which alone the flow\-matching loss is computed\.

We investigate the conditioning\-path design for multimodal conditional time\-series generation\. For modalitymm, the frozen encoder yields a latent sequenceH\(m\)=AEmenc​\(c\(m\),o\(m\)\)H^\{\(m\)\}=\\mathrm\{AE\}\_\{m\}^\{\\text\{enc\}\}\(c^\{\(m\)\},o^\{\(m\)\}\), which a bank ofnnlearnable per\-modality query tokensQ\(m\)Q^\{\(m\)\}summarizes by cross\-attention,A\(m\)=CrossAttn⁡\(Q\(m\),H\(m\),H\(m\)\)∈ℝn×dA^\{\(m\)\}=\\mathrm\{CrossAttn\}\(Q^\{\(m\)\},H^\{\(m\)\},H^\{\(m\)\}\)\\in\\mathbb\{R\}^\{n\\times d\}, givingM⋅nM\\\!\\cdot\\\!ntime\-variant condition tokens; a missing modality falls back to a per\-modality learnable missing\-token sequenceA~\(m\)∈ℝn×d\\widetilde\{A\}^\{\(m\)\}\\in\\mathbb\{R\}^\{n\\times d\}\. These tokens enter the generator in context\. How they are injected is a key design choice: learnable cross\-attention pooling outperforms plain in\-context tokens, modulation\-only injection, and an in\-painting alternative, especially on the harder ABP tasks \(Figure[4](https://arxiv.org/html/2608.12592#S3.F4)\)\. The static descriptor is likewise encoded \(with its missingness made visible\) into one or two tokens, depending on the cohort’s static schema, and injected through both routes, which together outperform either alone \(Table[3](https://arxiv.org/html/2608.12592#S3.T3)\)\.

The denoiser backbonefθf\_\{\\theta\}is a DiT/SiT\-style vision transformer\([31](https://arxiv.org/html/2608.12592#bib.bib26)\), trained with thexx\-predictionvv\-loss flow\-matching formulation\([21](https://arxiv.org/html/2608.12592#bib.bib27)\)\. With noiseϵ∼𝒩⁡\(0,σ2​I\)\\epsilon\\sim\\mathcal\{N\}\(0,\\sigma^\{2\}I\)andt∈\(0,1\)t\\in\(0,1\)from a logit\-normal schedule, we form the interpolantzt=t​Φ\+\(1−t\)​ϵz\_\{t\}=t\\,\\Phi\+\(1\-t\)\\,\\epsilonwith target velocityv⋆=Φ−ϵv^\{\\star\}=\\Phi\-\\epsilon; the network predicts the clean signalΦ^=fθ​\(zt,t,c\)\\widehat\{\\Phi\}=f\_\{\\theta\}\(z\_\{t\},t,c\), which givesv^=\(Φ^−zt\)/\(1−t\)\\widehat\{v\}=\(\\widehat\{\\Phi\}\-z\_\{t\}\)/\(1\-t\), and we minimize the mask\-normalized error𝔼Φ,ϵ,t​\[∥Φmask⊙\(v^−v⋆\)∥22/∥Φmask∥1\]\\mathbb\{E\}\_\{\\Phi,\\epsilon,t\}\\big\[\\lVert\\Phi\_\{\\text\{mask\}\}\\odot\(\\widehat\{v\}\-v^\{\\star\}\)\\rVert\_\{2\}^\{2\}/\\lVert\\Phi\_\{\\text\{mask\}\}\\rVert\_\{1\}\\big\]\. At inference we integrate the ODEd​zt/d​t=v^dz\_\{t\}/dt=\\widehat\{v\}from noise \(t=0t\{=\}0\) to data \(t=1t\{=\}1\) with a fixed number of Euler or second\-order Heun steps \(the last always Euler\), encoding the conditions once and mapping the final image back to a series with𝒟−1\\mathcal\{D\}^\{\-1\}\.

### 3Experiment

#### 3\.1Experiment Setup

##### Datasets and tasks

We evaluate on three tasks spanning two domains: one wearable/glycemic cohort and two critical\-care databases\. All windows are 24 hours at 5\-minute resolution \(T=288T\{=\}288\)\.\(i\) AI\-READI\([2](https://arxiv.org/html/2608.12592#bib.bib23)\), a multimodal type\-2\-diabetes cohort: we generate a subject’s CGM trace from four co\-recorded wearable modalities \(heart rate, calorie expenditure, physical activity, respiratory rate\) and static tabular clinical features\.\(ii\) MIMIC\-III\([16](https://arxiv.org/html/2608.12592#bib.bib24)\): we generate the mean ABP trace from three co\-recorded vitals \(heart rate, respiratory rate,SpO2\\mathrm\{SpO\}\_\{2\}\) and a static clinical vector, all taken from the Waveform Database Matched Subset numerics\.\(iii\) MIMIC\-IV\([15](https://arxiv.org/html/2608.12592#bib.bib25)\)poses the same task on a distinct cohort, but from bedside charted measurements rather than waveforms, giving a dual\-resolution setup with the sparsely charted vitals on an hourly grid \(Tcond=24T\_\{\\mathrm\{cond\}\}\{=\}24\)\.

##### Baselines

We compare against six representative conditional generators, grouped by the conditioning interface their architecture exposes; all generate the same target as ReCoGen\.*Signal\-conditioned:*Diffusion\-TS[37](https://arxiv.org/html/2608.12592#bib.bib21)and ImagenTime[27](https://arxiv.org/html/2608.12592#bib.bib22)stack the target and the co\-recorded series into one multivariate series and in\-paint the target, supervising the target channel only; neither admits a label or static features, so both consume the conditioning series alone\.*Attribute\-conditioned:*TimeWeaver[28](https://arxiv.org/html/2608.12592#bib.bib11)fuses the conditioning series as time\-varying metadata into a CSDI\-style denoiser, and WaveStitch[33](https://arxiv.org/html/2608.12592#bib.bib14)pins the co\-recorded channels as RePaint anchors on an SSSD\-S4 backbone; neither has a path for the tabular static vector\. We take both from ConTSG\-Bench\([18](https://arxiv.org/html/2608.12592#bib.bib37)\), a public benchmark whose ports condition on discrete attributes alone, and add back each paper’s own mechanism: TimeWeaver’s continuous metadata path and WaveStitch’s anchor conditioning\.*Text\-conditioned:*VerbalTS[8](https://arxiv.org/html/2608.12592#bib.bib17)and Bridge[20](https://arxiv.org/html/2608.12592#bib.bib19)accept text only, so we verbalize the complete conditioning set and embed it with a frozen LongCLIP text encoder; Bridge additionally draws a same\-label real target window as its prototype\. These two therefore receive our full conditioning set\. Per\-method settings are in the supplement\.

##### Fairness of the comparison

Everything outside that interface is held fixed: all baselines reuse our dataset builder, split, windowing and valid\-window filter verbatim, generate on the same evaluation windows, are scored by the same probe, and train for 1000 epochs at learning rate10−410^\{\-4\}with the optimizer of their reference implementation\. Each receives the largest subset of the conditioning set its architecture admits — complete for VerbalTS and Bridge, and Bridge in fact receives strictly more, since its prototype is a real target window\. That the other four cannot ingest heterogeneous static conditions is the limitation this work targets, not an artifact of our setup; Figure[4](https://arxiv.org/html/2608.12592#S3.F4)isolates it with an in\-painting variant of ReCoGen that changes only how the conditioning series enter\.

Generative baselinesReCoGenRef\.TaskMetricDiffusion\-TSImagenTimeVerbalTSBridgeTimeWeaverWaveStitchReal\-Valid∗*MIMIC\-III*: diagnosis and mortality prediction with ABP onlySepsisAUROC0\.5660\.5130\.5150\.5050\.5100\.5250\.6770\.633AUPRC0\.3600\.3160\.3210\.3110\.3150\.3240\.4940\.436HFAUROC0\.5230\.5180\.5010\.4930\.5030\.5030\.6500\.650AUPRC0\.2750\.2760\.2680\.2620\.2680\.2690\.4130\.408Mort\.AUROC0\.5190\.5010\.5110\.5150\.4970\.5530\.5990\.658AUPRC0\.1810\.1740\.1800\.1900\.1730\.2050\.2490\.316*MIMIC\-IV*: diagnosis and mortality prediction with ABP onlySepsisAUROC0\.5310\.5200\.5270\.4980\.5040\.4950\.6920\.657AUPRC0\.1750\.1770\.1680\.1540\.1600\.1620\.2860\.260HFAUROC0\.5000\.5100\.5010\.5030\.5030\.4980\.6370\.596AUPRC0\.2580\.2670\.2580\.2590\.2590\.2600\.3640\.330Mort\.AUROC0\.5040\.5600\.5060\.4840\.5190\.5350\.7020\.656AUPRC0\.1180\.1380\.1160\.1100\.1170\.1300\.2360\.209*AI\-READI*: study\_group prediction under 2 input modesStudy group\(CGM only\)AUROC0\.5020\.5190\.5460\.7150\.6560\.6040\.7710\.763AUPRC0\.2530\.2620\.2910\.4120\.3560\.3300\.5040\.477Study group\(CGM\+\+Lab\)AUROC0\.7590\.7570\.5520\.7940\.7900\.7770\.7950\.796AUPRC0\.4690\.4660\.2980\.5250\.5140\.5000\.5330\.525Table 1:Downstream evaluation under a train\-on\-real, test\-on\-synthetic protocol: a probe trained on real signals scores each method’s generated signal \(5\-seed mean\)\. MIMIC\-III/\-IV predict external ICD diagnoses \(sepsis, heart failure “HF”\) and in\-hospital mortality from the generated ABP; AI\-READI predicts four\-class study\_group from the generated CGM alone or with lab test results\. Bold marks the best generative method per row\.
##### Evaluation protocol

Because no ground\-truth “clean” target exists for held\-out subjects, we assess generation quality by downstream clinical utility rather than by point\-wise reconstruction error\. Following a train\-on\-real, test\-on\-synthetic protocol, a classifier trained on real signals scores each method’s generated signals against their true labels; every method faces the same probe, so results are directly comparable, and each metric is the mean over five classifier seeds \(per\-seed standard deviations and significance tests are in the supplement\)\. Because two of the downstream labels \(in\-hospital mortality on MIMIC and study\_group on AI\-READI\) would otherwise be model inputs, we remove the categorical label from the conditioning set of*every*method and retrain, so no reported number is scored on a label its generator was given\. We also score the real validation signals under the same probe \(Real\-Valid∗\) and treat this as an approximate anchor rather than an upper bound: it is itself a finite\-sample estimate, and a generated signal can score above it\. The downstream tasks are four\-class study\_group classification on AI\-READI — from the generated CGM alone and with the real labs fused into the probe input — and, on MIMIC\-III/\-IV, external ICD diagnoses \(*sepsis*,*heart failure*\) plus in\-hospital*mortality*from the generated ABP alone\.

#### 3\.2Main Results

ReCoGen is the strongest generative model in every row of Table[1](https://arxiv.org/html/2608.12592#S3.T1), attaining the best AUROC and AUPRC on all sixteen \(dataset, task, metric\) combinations\. The margin is largest on the critical\-care benchmarks, where recovering diagnoses and mortality from the ABP waveform alone is hard and the six baselines hover near chance; on AI\-READI our generated CGM leads clearly without the real labs and matches the strongest baseline once they are fused in, where every method saturates because the real labs dominate the probe\. Against theReal\-Valid∗reference obtained from the real signal under the same probe, ReCoGen reaches or exceeds it on thirteen of the sixteen rows and falls below it on three, most visibly on MIMIC\-III mortality \(AUROC0\.5990\.599vs\.0\.6580\.658, AUPRC0\.2490\.249vs\.0\.3160\.316\)\.

##### A qualitative look on AI\-READI

Figure[3](https://arxiv.org/html/2608.12592#S3.F3)is an illustration rather than added evidence, and it covers one dataset\. study\_group is ordinal and the real CGM class means span5252mg/dL, so the class structure is legible in the waveform itself: ReCoGen reproduces the ordering and most of the span \(4747mg/dL\), while Bridge compresses the classes to3737mg/dL and shifts the whole cohort upward\. We plot class means because the variability between participants of one class is far larger than the separation between classes\. The same plot on MIMIC would show little, since the real ABP level separates the ICU labels by only a few mmHg; there the comparison rests on Table[1](https://arxiv.org/html/2608.12592#S3.T1), and we make no visual claim\.

Figure 3:Generated CGM reproduces the class structure of the real signal on AI\-READI\. Each curve is the 24\-hour trace averaged over the held\-out participants of one study\_group class; the vertical axis is mean glucose in mg/dL, shared across panels, and “spread” is the gap between the highest and lowest class mean\. Bridge is the strongest baseline on this dataset\.DatasetTaskFull−\-TS−\-staticRealMIMIC\-IIISepsis0\.6770\.5790\.5000\.633HF0\.6500\.6180\.5440\.650Mortality0\.5990\.5700\.5210\.658MIMIC\-IVSepsis0\.6920\.6560\.5870\.657HF0\.6370\.6080\.5160\.596Mortality0\.7020\.5610\.5650\.656AI\-READIStudy Group0\.7710\.7500\.5070\.763

Table 2:Conditioning ablation: ReCoGen retrained with all conditions \(Full\), without the time\-series conditions \(−\-TS\), or without the static ones \(−\-static\), Each ablated model is retrained and re\-scored end to end by the same train\-on\-real, test\-on\-synthetic probe \(AUROC, 5\-seed mean\); Full and Real repeat the corresponding values of Table[1](https://arxiv.org/html/2608.12592#S3.T1)\. Underline marks the more damaging removal per row\.

##### What the protocol does and does not establish

The probe scores a generated signal, and that signal is a function of the conditions, so a high score can arise in two ways: the synthesized target carries the same label\-relevant physiology as the real one, or the generator re\-expresses information already in the conditions in a form the probe reads easily\. Downstream utility therefore measures label\-relevant information transfer, and conflates target fidelity with condition re\-expression\. We add no pointwise fidelity metric because the setting offers no clean target: the signal we synthesize for a held\-out subject is precisely the one that was not measured\. Two observations bound the ambiguity\. Sepsis and heart failure are external ICD diagnoses never available to the generator, so recovering them from the generated waveform cannot be explained by*copying*a conditioning variable; they can still be correlated with the covariates it does see\. Mortality is the sharper case: driven by the hemodynamic state ABP encodes and correlated with those covariates, it is the label most exposed to a conditioning\-correlated shortcut\. Table[2](https://arxiv.org/html/2608.12592#S3.T2)bounds that room: static conditions alone already support much of the score \(MIMIC\-IV sepsis AUROC0\.6560\.656with no time\-series condition\)\. Scores aboveReal\-Valid∗are thus evidence that label\-relevant structure survives generation, possibly in a cleaner form than the measured waveform, not that the synthetic signal is the more faithful one\.

#### 3\.3Ablation Study

Figure 4:Time\-series conditioning mechanism: per\-task downstream AUROC \(bars: 5\-seed mean; error bars:±1\\pm 1std\) for four injections differing only in how the conditioning series enters — frozen\-AE latents via learnable cross\-attention tokens \(ReCoGen\), the same latents as in\-context tokens, the pooled latents as one AdaLN vector, and RePaint\-style in\-painting \(no AE\)\. Dashed line: chance\.##### Time\-series vs\. static conditioning

To quantify how much each conditioning group contributes, we retrain ReCoGen leave\-one\-group\-out \(Table[2](https://arxiv.org/html/2608.12592#S3.T2)\): from the “Full” conditioning we drop either all time\-series conditions \(−\-TS\) or all static/tabular ones \(−\-static\), applying the ablation identically at training, validation and generation time\. Removing either group lowers AUROC on every task, so both carry information that ReCoGen transfers into its generation; dropping the static conditions hurts more in most cases\.

DatasetTaskToken\+\+AdaLN\(ReCoGen\)Token\-onlyAdaLN\-onlyMIMIC\-IIISepsis0\.6770\.5470\.595HF0\.6500\.5360\.648Mortality0\.5990\.5250\.561MIMIC\-IVSepsis0\.6920\.5600\.562HF0\.6370\.5510\.593Mortality0\.7020\.5010\.509AI\-READIStudy group0\.7710\.6240\.742

Table 3:Static\-feature encoding ablation as a token×\\timesAdaLN factorial, per\-task downstream AUROC: in\-context tokens\+\+AdaLN context \(ReCoGen\) vs\. tokens\-only vs\. AdaLN\-only\. Bold marks the best injection per row\.

Figure 5:Stage\-I mask\-ratio sensitivity\. Downstream AUROC against the stage\-I mask ratio; each line is the mean over a dataset’s tasks \(AI\-READI: study\_group; MIMIC\-III/\-IV: sepsis, HF, mortality\), error bars the pooled55\-seed probe std\. The sweep is a single end\-to\-end re\-run, so itsρ=0\.3\\rho\{=\}0\.3point need not reproduce the main table exactly\.

##### Time\-series conditioning mechanism

Holding everything else fixed, we compare four ways for the conditioning series to enter \(Figure[4](https://arxiv.org/html/2608.12592#S3.F4)\): frozen\-AE latents read by learnable per\-modality queries via*cross\-attention*into in\-context tokens \(ReCoGen\); the same latents as plain in\-context tokens; the pooled latents through AdaLN modulation; and the in\-painting alternative of Diffusion\-TS\([37](https://arxiv.org/html/2608.12592#bib.bib21)\)and ImagenTime\([27](https://arxiv.org/html/2608.12592#bib.bib22)\)\. Cross\-attention wins overall, most clearly on the ABP tasks, where the other injections fall well behind and in\-painting is unstable, dropping toward or below chance on the hardest cases \(e\.g\.MIMIC\-IV mortality\)\. On AI\-READI all four are comparable\.

##### Static\-feature encoding

We inject the static features as a token×\\timesAdaLN factorial \(Table[3](https://arxiv.org/html/2608.12592#S3.T3), same protocol\): in\-context tokens plus a pooled AdaLN modulation \(ReCoGen\), tokens only, or the AdaLN modulation alone\. Both paths together win on every \(dataset, task\), by a wide margin on MIMIC\-IV, so they are complementary rather than redundant; between the single\-path variants, removing the AdaLN modulation is consistently more damaging\. The static features are therefore carried primarily through AdaLN, the token adding a complementary gain only when that path is present\.

##### Stage\-I mask\-ratio sensitivity

The stage\-I autoencoders hold out and reconstruct an additional fraction of the observed points, the*mask ratio*, set to0\.30\.3in ReCoGen\. Sweeping it over\{0,0\.1,0\.3,0\.5,0\.7\}\\\{0,0\.1,0\.3,0\.5,0\.7\\\}and retraining both stages end to end per value \(Figure[5](https://arxiv.org/html/2608.12592#S3.F5), AUROC averaged over each dataset’s tasks\), the generator is fairly robust: AUROC varies within a modest range with no monotone trend, and0\.30\.3is a consistently strong setting\.

### 4Related Works

##### Conditional Time\-Series Generation

We review existing generators through the lens of how they ingest conditioning signals\.1\)Label\-conditioned models steer generation with a discrete class: TTS\-CGAN[22](https://arxiv.org/html/2608.12592#bib.bib10)and TimeVQVAE[19](https://arxiv.org/html/2608.12592#bib.bib12)fall into this category\.2\)Attribute\-conditioned models condition on structured metadata: TEdit[14](https://arxiv.org/html/2608.12592#bib.bib13)and WaveStitch[33](https://arxiv.org/html/2608.12592#bib.bib14)are two representative works\. TimeWeaver[28](https://arxiv.org/html/2608.12592#bib.bib11)extends this line of work by enabling multimodal conditioning through the tokenization and fusion of heterogeneous covariates spanning categorical, continuous, and time\-variant modalities\.3\)Text\-conditioned models verbalize the condition into natural language and inject it through text embedding models: VerbalTS[8](https://arxiv.org/html/2608.12592#bib.bib17), T2S[7](https://arxiv.org/html/2608.12592#bib.bib18), Bridge[20](https://arxiv.org/html/2608.12592#bib.bib19), and DiffuSETS[17](https://arxiv.org/html/2608.12592#bib.bib15)are in this group\.4\)Signal\-conditioned models take the observed portion of a time series as the condition, prediction and imputation being the representative tasks: CSDI[34](https://arxiv.org/html/2608.12592#bib.bib20), Diffusion\-TS[37](https://arxiv.org/html/2608.12592#bib.bib21), and ImagenTime[27](https://arxiv.org/html/2608.12592#bib.bib22)\. Across all four groups, a generator is tailored to*one*kind of condition and absorbs it directly into the generative process, either as an in\-context sequence to be in\-painted alongside the target or as fused metadata; even TimeWeaver[28](https://arxiv.org/html/2608.12592#bib.bib11), which admits multiple covariate types, assumes them densely aligned and does not model the heavy, modality\-dependent missingness of co\-recorded physiological streams\. ReCoGen departs from this recipe in two ways: it targets genuinely multimodal conditioning \(several irregularly sampled, partially observed time series together with static clinical descriptors\) rather than a single condition type, and it decouples*how a condition is represented*from*how the target is generated*, freezing a missingness\-aware encoder per modality so the generator consumes robust condition tokens instead of reconstructing the raw streams itself\.

##### Medical Downstream Tasks

Our probe is trained on real signals, which is meaningful only if the labels are ones those signals genuinely predict; we therefore ground each task in prior work\. CGM traces routinely characterize glycemic state and screen for diabetes\([9](https://arxiv.org/html/2608.12592#bib.bib4)\), and CGMformer\([25](https://arxiv.org/html/2608.12592#bib.bib5)\)fine\-tunes exactly the diabetes\-status target \(study\_group\) we probe on AI\-READI\. ABP and its co\-recorded vitals are the core input to ICU risk prediction: MIMIC benchmarks predict in\-hospital mortality from clinical time series\([10](https://arxiv.org/html/2608.12592#bib.bib1)\),[29](https://arxiv.org/html/2608.12592#bib.bib6)predict sepsis onset from routine vitals, and others predict circulatory failure and hypotension from the same signals\([13](https://arxiv.org/html/2608.12592#bib.bib2);[11](https://arxiv.org/html/2608.12592#bib.bib3)\)\. Our three ABP labels are complementary: mortality is the canonical ICU outcome, directly driven by the hemodynamic state ABP encodes\([36](https://arxiv.org/html/2608.12592#bib.bib7);[26](https://arxiv.org/html/2608.12592#bib.bib8);[3](https://arxiv.org/html/2608.12592#bib.bib9)\), while sepsis and heart failure are external diagnoses never given to the generator, so they test whether it preserves label\-relevant physiology rather than low\-order statistics\.

### 5Conclusion

ReCoGen addresses conditional generation of physiological time series from several irregularly sampled, partially observed signals together with static clinical variables\. Feeding them straight into the generator makes one objective both represent the conditions and generate the target, serving neither well; ReCoGen separates the two, distilling each irregular stream into missingness\-tolerant tokens with a per\-modality masked autoencoder and generating the target with a frozen\-encoder flow\-matching model\. It attains the best downstream utility on all sixteen \(dataset, task, metric\) settings across AI\-READI, MIMIC\-III and MIMIC\-IV, by the widest margin on the critical\-care ABP benchmarks where the six baselines hover near chance\. Two limitations frame that result: downstream utility conflates target fidelity with a re\-expression of the conditions, so the real\-signal reference is an anchor rather than a ceiling; and encoding each modality independently leaves cross\-modal dependencies to the generator\. Modeling the conditions jointly, and separating fidelity from re\-expression in a paired setting, are natural next steps\.

### Acknowledgment

This research was partially funded by the National Institutes of Health \(NIH\) under award 1R01EB037101\-01\. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the NIH\.

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- Yuan and Qiao \(2024\)X\. Yuan and Y\. QiaoDiffusion\-ts: interpretable diffusion for general time series generation\.arXiv Preprint arXiv:2403\.01742\.Cited by:[§1](https://arxiv.org/html/2608.12592#S1.p3.1),[§1](https://arxiv.org/html/2608.12592#S1.p4.1),[§3\.1](https://arxiv.org/html/2608.12592#S3.SS1.SSS0.Px2.p1.1),[§3\.3](https://arxiv.org/html/2608.12592#S3.SS3.SSS0.Px2.p1.1),[§4](https://arxiv.org/html/2608.12592#S4.SS0.SSS0.Px1.p1.1)\.

## Appendix

This supplement lists the full parameter settings behind every number reported in the main paper: the windowing and preprocessing of the three cohorts, the Stage I masked autoencoders, the Stage II conditional flow\-matching generator, the sampling configuration, the six baselines, and the downstream evaluation probe\. Values that a launch script leaves unset are the corresponding reference implementation’s defaults\. All runs use a single NVIDIA GPU per job\.

### Appendix AData Windowing and Preprocessing

Every method in a given benchmark consumes exactly the same windows: the baselines call the dataset builder, split, windowing and valid\-window filter of ReCoGen verbatim, and generation is driven by the same window index \(the metadata file written by our own generation pass\), so the downstream probe scores all methods on an identical set of subjects and time intervals\. Each channel is min\-max normalized to\[−1,1\]\[\-1,1\]per series, and each per\-modality pack carries a binary observed mask \(11= observed,00= missing or padding\)\.

##### AI\-READI \(CGM generation\)

Windows are built on the glucose anchor grid: anchor sampling period55minutes with a22s matching tolerance, maximum anchor gap1010minutes, maximum window span2424hours, and at least288288events per day, givingT=288T\{=\}288steps per window\. Windows whose target exceeds a0\.50\.5missing ratio are discarded\. The four conditioning modalities \(heart rate, calorie expenditure, physical activity, respiratory rate\) are aligned to that grid; the static descriptor consists of66numeric CGM\-enhanced features,66self\-report binary flags \(yes/no/unknown\), and66“past two weeks” medication labels\. The44\-class study\_group is the downstream target, not a condition \(see “Label conditioning is disabled” below\)\.

##### MIMIC\-III and MIMIC\-IV \(ABP generation\)

Stays are split80/2080/20into train and test by train\_frac=0\.8\{=\}0\.8; a window is kept if at least5%5\\%of its target steps are observed \(min\_target\_coverage=0\.05\{=\}0\.05\) and its missing ratio does not exceed0\.50\.5\. The target is the mean ABP channel on a2424\-hour,55\-minute grid \(T=288T\{=\}288\)\. On MIMIC\-III the ABP and the three vitals \(heart rate, respiratory rate,SpO2\\mathrm\{SpO\}\_\{2\}\) come from the Waveform Database Matched Subset numerics resampled onto that grid; on MIMIC\-IV they come from bedside charted measurements, with the vitals kept on the coarser hourly grid \(Tcond=24T\_\{\\mathrm\{cond\}\}\{=\}24\)\. The static descriptor is a2727\-dimensional vector \(age, gender, and2525chart/lab/drug window means\); the binary in\-hospital\-mortality label is likewise a downstream target, not a condition\.

### Appendix BStage I: Per\-Modality Masked Autoencoders

One autoencoder is trained per time\-variant conditioning modality \(four on AI\-READI, three on each MIMIC cohort\) with the settings in Table[5](https://arxiv.org/html/2608.12592#A2.T5)\. The network projects the \(single\-channel\) input todmodeld\_\{\\text\{model\}\}, adds sinusoidal positional encodings, replaces every naturally missing or additionally held\-out step with one shared learnable \[missing\] token, applies a Transformer encoder, and reads out with a linear head\. The loss is the mean squared error on the additionally held\-out steps only; the mask ratioρ\\rhois the fraction of*observed*steps that are held out\. The checkpoint with the lowest validation loss is kept and frozen for Stage II\.

SettingAI\-READIMIMICModel dimensiondmodeld\_\{\\text\{model\}\}128128Attention heads44Encoder layers33Input series lengthLL288288 / 24Positional\-encoding capacity288512Mask ratioρ\\rho0\.30\.3Epochs10001000Batch size256256OptimizerAdamWAdamWLearning rate3×10−43\{\\times\}10^\{\-4\}3×10−43\{\\times\}10^\{\-4\}Weight decay10−410^\{\-4\}10−410^\{\-4\}Max\. missing ratio \(filter\)0\.50\.1Seed00

Table 4:Stage I masked\-autoencoder settings\. One model is trained per conditioning modality; the mask\-ratio sweep of the main paper retrains all of them atρ∈\{0,0\.1,0\.3,0\.5,0\.7\}\\rho\\in\\\{0,0\.1,0\.3,0\.5,0\.7\\\}\. The conditioning series areL=288L\{=\}288steps long on MIMIC\-III \(5\-minute grid\) andL=24L\{=\}24on MIMIC\-IV \(hourly grid\); the positional\-encoding table is simply sized to cover them\.
SettingAI\-READIMIMIC*Backbone \(JiT\)*Image size \(delay embedding\)1818Patch size22Hidden size128128Depth44Attention heads44Attn\./proj\. dropout0\.1 / 0\.10\.1 / 0\.1Bottleneck dimension6464Label classes42In\-context tokens1813*Condition encoder*Tokens per modality44Encoder width / heads128 / 4128 / 4Frozen AE \(dim/heads/layers\)128/4/3128/4/3*Flow matching and optimization*PmeanP\_\{\\text\{mean\}\}/PstdP\_\{\\text\{std\}\}0\.5 / 1\.20 / 1\.2ttclampϵt\\epsilon\_\{t\}10−510^\{\-5\}10−510^\{\-5\}Noise scale1\.01\.0Label drop prob\.0\.00\.0EMA decays0\.999 and 0\.9999Epochs10001000Batch size256256OptimizerAdamWAdamWLearning rate10−410^\{\-4\}10−410^\{\-4\}Weight decay10−510^\{\-5\}10−510^\{\-5\}Gradient clipping1\.01\.0Seed4242*Sampling*ODE solverHeunHeunSampling steps5050Guidance scale1\.01\.0ttinterval\[0,1\]\[0,1\]\[0,1\]\[0,1\]Weights / epochEMA\(0\.9990\.999\), epoch 1000

Table 5:Stage II generator settings\.PmeanP\_\{\\text\{mean\}\}is the only value that differs between cohorts; it was selected on validation utility in a per\-cohort sweep, with everything else held fixed\.

### Appendix CStage II: Conditional Flow\-Matching Generator

Stage II freezes the Stage I encoders and trains the JiT denoiser with the settings in Table[5](https://arxiv.org/html/2608.12592#A2.T5)\. AT=288T\{=\}288series is delay\-embedded into an18×1818\\times 18single\-channel image \(non\-overlapping windows, i\.e\. delay=\{=\}embedding=\{=\}image size\) and the flow\-matching loss is computed only inside the valid\-region mask\. Each conditioning modality contributes44in\-context tokens produced by learnable per\-modality queries cross\-attending over its frozen latents; the static descriptor contributes22further tokens on AI\-READI \(one numeric MLP token and one categorical\-transformer token\) and11on the MIMIC cohorts, and is additionally pooled into the AdaLN modulation\. The in\-context stream therefore has length4×4\+2=184\{\\times\}4\{\+\}2\{=\}18on AI\-READI and3×4\+1=133\{\\times\}4\{\+\}1\{=\}13on MIMIC, and is inserted before the first transformer block \(in\_context\_start=0\{=\}0\)\. Two exponential moving averages of the weights are tracked; all reported numbers use the faster one \(decay0\.9990\.999\) at epoch10001000\.

##### Label conditioning is disabled

Both downstream label sets \(in\-hospital mortality on the MIMIC cohorts, the44\-class study\_group on AI\-READI\) would leak if they also conditioned the generator, so the categorical label is removed from*every*method and all label\-conditioned models are retrained from scratch\. For ReCoGen this means the label embedding is pinned to its null slot identically at training, validation and generation time, so the true label never reaches the network; the “Label classes” row of Table[5](https://arxiv.org/html/2608.12592#A2.T5)therefore sizes an embedding that is never driven by a real label\. Among the baselines, TimeWeaver’s categorical metadata attribute is held constant, the verbalization fed to VerbalTS and Bridge omits the outcome clause, and Diffusion\-TS, ImagenTime and WaveStitch never had a label path to begin with\. Every number reported in the main paper comes from this de\-leaked setting\.

##### Ablation variants

All ablations reuse Table[5](https://arxiv.org/html/2608.12592#A2.T5)and change exactly one component\. The conditioning ablations \(−\-TS,−\-static\) replace a group with the model’s built\-in missing representation \(zeroed values and masks, or the null label slot\), so tensor shapes and the in\-context length stay fixed, and the ablation is applied identically at training, validation and generation time\. The injection variants \(in\-context tokens without cross\-attention, AdaLN\-only pooling, RePaint\-style in\-painting\) and the static\-encoding factorial \(Token\+\+AdaLN, Token\-only, AdaLN\-only\) likewise keep every other setting\. Each variant is retrained from scratch; the mask\-ratio sweep retrains both stages end to end per value\.

### Appendix DBaselines

MethodSettingsDiffusion\-TSdmodel=128d\_\{\\text\{model\}\}\{=\}128;33encoder /44decoder layers;10001000diffusion steps,200200sampling stepsImagenTimedelay=\{=\}embedding=32\{=\}32\(32×3232\\times 32image\);UNet width6464;100100diffusion stepsTimeWeaverchannels6464,44layers,88heads; cosine schedule;10001000diffusion steps; metadata:cond=128\\text\{cond\}\{=\}128,token=64\\text\{token\}\{=\}64,22fusion layers,44fusion headsWaveStitchSSSD\-S4: residual/skip channels6464,44residuallayers, state size6464, cond\. channels1616;200200diffusion stepsVerbalTSchannels6464,44layers, AdaLN text conditioning;cosine schedule,10001000diffusion stepsBridgeUNet width6464,22residual blocks per stage;cosine schedule,10001000diffusion steps; prototypeseries drawn from the training splitTable 6:Baseline settings shared by the three benchmarks\. Unlisted values are the reference implementation’s defaults\.All six baselines are trained for10001000epochs at learning rate10−410^\{\-4\}on the same windows, with the seed fixed to4242and the target reduced to the single generated channel\. Batch size is512512for Diffusion\-TS, ImagenTime and TimeWeaver and256256for WaveStitch, VerbalTS and Bridge\. Five of the six use Adam \(β=\(0\.9,0\.96\)\\beta\{=\}\(0\.9,0\.96\)\); ImagenTime keeps AdamW, as in its reference implementation\. Method\-specific settings are listed in Table[6](https://arxiv.org/html/2608.12592#A4.T6); for the text\-conditioned pair, the verbalized condition is embedded by a frozen LongCLIP text tower \(768768\-d,248248\-token window\) in which each conditioning series is rendered as summary statistics plus a2020\-point downsampled numeric transcript in physical units\.

### Appendix EDownstream Evaluation Protocol

The probe is a 1D CNN: three convolutional blocks with kernel sizes77,55and33and6464,128128and256256channels, each with batch normalization and ReLU and the first two followed by max pooling, then global average pooling, dropout0\.20\.2and a linear classifier\. It is trained on*real*signals for5050epochs with Adam, learning rate10−310^\{\-3\}, weight decay10−410^\{\-4\}and batch size256256, and then applied to each method’s*generated*signals\. Every reported metric is the mean \(and standard deviation\) over the five probe seeds\{0,1,2,3,4\}\\\{0,1,2,3,4\\\}; the same trained probe configuration scores every method, and the real validation signals scored under it give theReal\-Valid∗reference\. In the fused AI\-READI mode the generated CGM passes through the same convolutional trunk while the biochemical lab values and their missingness mask pass through a two\-layer MLP \(width6464, dropout0\.20\.2\); the two embeddings are concatenated before the linear classifier head\. The MIMIC cohorts are reported in the ABP\-only mode\.

### Appendix FStatistical Significance of the Main Results

The main paper reports 5\-seed means\. Table[7](https://arxiv.org/html/2608.12592#A6.T7)adds the per\-seed dispersion behind every AUROC entry of that table and tests ReCoGen’s margin over each baseline; Table[9](https://arxiv.org/html/2608.12592#A6.T9)isolates the comparison against the*strongest*rival in each setting, and Table[9](https://arxiv.org/html/2608.12592#A6.T9)aggregates across settings\.

##### Test protocol

The unit of replication is the downstream probe seed: all methods are scored by the same probe configuration re\-trained under the five seeds\{0,1,2,3,4\}\\\{0,1,2,3,4\\\}, givingn=5n\{=\}5AUROC values per \(dataset, task, method\)\. For each of the eight \(dataset, task\) settings we compare ReCoGen against each of the six baselines with a two\-sided Welchtt\-test \(unequal variances, Satterthwaite degrees of freedom\) and control the family\-wise error rate across the six comparisons within that setting by the Holm–Bonferroni procedure;∗,∗∗and∗∗∗in Table[7](https://arxiv.org/html/2608.12592#A6.T7)denote Holm\-adjustedp<0\.05p<0\.05,p<0\.01p<0\.01andp<0\.001p<0\.001\. To summarize across settings without assuming normality, we also run an exact Wilcoxon signed\-rank test on the eight paired per\-setting AUROC differences \(Table[9](https://arxiv.org/html/2608.12592#A6.T9)\); withn=8n\{=\}8its smallest attainable two\-sidedpp\-value is2/28=0\.00782/2^\{8\}=0\.0078, which every baseline attains\.

##### Result

ReCoGen’s margin is significant after Holm correction in 46 of the 48 per\-setting comparisons\. The two exceptions are both on AI\-READI in the CGM\+\+Lab mode, against Bridge \(\+0\.001\+0\.001,p=0\.69p\{=\}0\.69\) and TimeWeaver \(\+0\.005\+0\.005,p=0\.38p\{=\}0\.38\): once the real laboratory values are fused into the probe input every method saturates near the real\-signal reference, so that mode does not separate generators\. In the CGM\-only mode on the same cohort the margin over the strongest baseline is\+0\.056\+0\.056and significant\. The single narrowest*significant*margin is MIMIC\-III mortality against WaveStitch \(\+0\.046\+0\.046,p=0\.009p\{=\}0\.009\), which is also the setting where ReCoGen falls furthest below the real\-signal reference\. Across settings, ReCoGen beats every baseline in8/88/8settings with median margins of\+0\.137\+0\.137to\+0\.165\+0\.165AUROC\.

##### What these tests do and do not cover

Five limitations should be read alongside the numbers\.\(i\)Only AUROC is tested; the per\-seed dispersion of AUPRC was not retained by the evaluation pipeline, so the AUPRC rows of the main table carry no test\.\(ii\)The five probe seeds are shared across methods, so the observations are in fact paired; we nevertheless use the unpaired Welch test, which discards that pairing and is therefore the conservative choice — a paired test would yield smallerpp\-values\.\(iii\)The tests are computed from means and standard deviations stored to three decimal places, so for the lowest\-variance entries \(subscript\.001\.001\) thettstatistics should be read as orders of magnitude rather than exact values; none of the Holm\-adjusted conclusions turns on those rows\.\(iv\)On AI\-READI, ReCoGen was scored by its own five\-seed probe instance rather than the one used for the baselines; the two agree on the real validation signal to within0\.0050\.005AUROC \(0\.7660\.766vs\.0\.7630\.763in CGM\-only,0\.7980\.798vs\.0\.7960\.796in CGM\+\+Lab\), and the main paper quotes the baseline probe’s value as the reference, but the AI\-READI comparisons are across probe draws rather than within one\.\(v\)TheReal\-Valid∗reference is not tested: its per\-seed dispersion was not retained either, and, as the main paper argues, it is an approximate anchor rather than a null hypothesis worth rejecting\.

Generative baselinesRef\.DatasetTaskDiffusion\-TSImagenTimeVerbalTSBridgeTimeWeaverWaveStitchReCoGenReal\-Valid∗MIMIC\-IIISepsis\.566∗∗∗\.010\.566^\{\\ast\\ast\\ast\}\_\{\.010\}\.513∗∗∗\.008\.513^\{\\ast\\ast\\ast\}\_\{\.008\}\.515∗∗∗\.004\.515^\{\\ast\\ast\\ast\}\_\{\.004\}\.505∗∗∗\.003\.505^\{\\ast\\ast\\ast\}\_\{\.003\}\.510∗∗∗\.003\.510^\{\\ast\\ast\\ast\}\_\{\.003\}\.525∗∗∗\.005\.525^\{\\ast\\ast\\ast\}\_\{\.005\}\.677\.019\\mathbf\{\.677\}\_\{\.019\}\.633HF\.523∗∗∗\.002\.523^\{\\ast\\ast\\ast\}\_\{\.002\}\.518∗∗∗\.004\.518^\{\\ast\\ast\\ast\}\_\{\.004\}\.501∗∗∗\.003\.501^\{\\ast\\ast\\ast\}\_\{\.003\}\.493∗∗∗\.002\.493^\{\\ast\\ast\\ast\}\_\{\.002\}\.503∗∗∗\.003\.503^\{\\ast\\ast\\ast\}\_\{\.003\}\.503∗∗∗\.002\.503^\{\\ast\\ast\\ast\}\_\{\.002\}\.650\.015\\mathbf\{\.650\}\_\{\.015\}\.650Mortality\.519\.008∗⁣∗\.519^\{\\ast\\ast\}\_\{\.008\}\.501\.006∗⁣∗\.501^\{\\ast\\ast\}\_\{\.006\}\.511\.006∗⁣∗\.511^\{\\ast\\ast\}\_\{\.006\}\.515\.003∗⁣∗\.515^\{\\ast\\ast\}\_\{\.003\}\.497\.004∗⁣∗\.497^\{\\ast\\ast\}\_\{\.004\}\.553\.012∗⁣∗\.553^\{\\ast\\ast\}\_\{\.012\}\.599\.024\\mathbf\{\.599\}\_\{\.024\}\.658MIMIC\-IVSepsis\.531∗∗∗\.006\.531^\{\\ast\\ast\\ast\}\_\{\.006\}\.520∗∗∗\.004\.520^\{\\ast\\ast\\ast\}\_\{\.004\}\.527∗∗∗\.013\.527^\{\\ast\\ast\\ast\}\_\{\.013\}\.498∗∗∗\.002\.498^\{\\ast\\ast\\ast\}\_\{\.002\}\.504∗∗∗\.007\.504^\{\\ast\\ast\\ast\}\_\{\.007\}\.495∗∗∗\.013\.495^\{\\ast\\ast\\ast\}\_\{\.013\}\.692\.007\\mathbf\{\.692\}\_\{\.007\}\.657HF\.500∗∗∗\.002\.500^\{\\ast\\ast\\ast\}\_\{\.002\}\.510∗∗∗\.001\.510^\{\\ast\\ast\\ast\}\_\{\.001\}\.501∗∗∗\.001\.501^\{\\ast\\ast\\ast\}\_\{\.001\}\.503∗∗∗\.001\.503^\{\\ast\\ast\\ast\}\_\{\.001\}\.503∗∗∗\.002\.503^\{\\ast\\ast\\ast\}\_\{\.002\}\.498∗∗∗\.007\.498^\{\\ast\\ast\\ast\}\_\{\.007\}\.637\.005\\mathbf\{\.637\}\_\{\.005\}\.596Mortality\.504∗∗∗\.016\.504^\{\\ast\\ast\\ast\}\_\{\.016\}\.560∗∗∗\.007\.560^\{\\ast\\ast\\ast\}\_\{\.007\}\.506∗∗∗\.002\.506^\{\\ast\\ast\\ast\}\_\{\.002\}\.484∗∗∗\.003\.484^\{\\ast\\ast\\ast\}\_\{\.003\}\.519∗∗∗\.012\.519^\{\\ast\\ast\\ast\}\_\{\.012\}\.535∗∗∗\.017\.535^\{\\ast\\ast\\ast\}\_\{\.017\}\.702\.005\\mathbf\{\.702\}\_\{\.005\}\.656AI\-READISG \(CGM\)\.502∗∗∗\.002\.502^\{\\ast\\ast\\ast\}\_\{\.002\}\.519∗∗∗\.003\.519^\{\\ast\\ast\\ast\}\_\{\.003\}\.546∗∗∗\.008\.546^\{\\ast\\ast\\ast\}\_\{\.008\}\.715∗∗∗\.003\.715^\{\\ast\\ast\\ast\}\_\{\.003\}\.656∗∗∗\.008\.656^\{\\ast\\ast\\ast\}\_\{\.008\}\.604∗∗∗\.015\.604^\{\\ast\\ast\\ast\}\_\{\.015\}\.771\.013\\mathbf\{\.771\}\_\{\.013\}\.763SG \(CGM\+\+Lab\)\.759∗∗∗\.006\.759^\{\\ast\\ast\\ast\}\_\{\.006\}\.757∗∗∗\.005\.757^\{\\ast\\ast\\ast\}\_\{\.005\}\.552∗∗∗\.012\.552^\{\\ast\\ast\\ast\}\_\{\.012\}\.794\.005\.794^\{\\phantom\{\\ast\}\}\_\{\.005\}\.790\.007\.790^\{\\phantom\{\\ast\}\}\_\{\.007\}\.777\.010∗\.777^\{\\ast\}\_\{\.010\}\.795\.002\\mathbf\{\.795\}\_\{\.002\}\.796Table 7:Downstream AUROC over the five probe seeds, writtenmeanstd\\text\{mean\}\_\{\\text\{std\}\}with leading zeros omitted; the means are exactly the AUROC rows of the main downstream table\. Superscripts on a baseline mark the Holm\-adjusted significance of ReCoGen’s margin over that baseline within its row \(two\-sided Welchtt\-test,n=5n\{=\}5per method, six comparisons per row\):∗p<0\.05\{\}^\{\\ast\}p<0\.05,p∗⁣∗<0\.01\{\}^\{\\ast\\ast\}p<0\.01,∗∗∗p<0\.001\{\}^\{\\ast\\ast\\ast\}p<0\.001; no superscript means not significant at0\.050\.05\. TheReal\-Valid∗reference is a single value per row — its per\-seed dispersion was not retained — and is not tested\.SettingRivalΔ\\DeltapHolmp\_\{\\mathrm\{Holm\}\}MIMIC\-III SepsisDiffusion\-TS\+0\.111\+0\.111<10−4<10^\{\-4\}MIMIC\-III HFDiffusion\-TS\+0\.127\+0\.127<10−5<10^\{\-5\}MIMIC\-III Mort\.WaveStitch\+0\.046\+0\.0460\.0090\.009MIMIC\-IV SepsisVerbalTS\+0\.165\+0\.165<10−7<10^\{\-7\}MIMIC\-IV HFImagenTime\+0\.127\+0\.127<10−7<10^\{\-7\}MIMIC\-IV Mort\.WaveStitch\+0\.167\+0\.167<10−6<10^\{\-6\}AI\-READI SGBridge\+0\.056\+0\.056<10−4<10^\{\-4\}AI\-READI SG\+\+LabBridge\+0\.001\+0\.0010\.6940\.694

Table 8:ReCoGen against the hardest baseline in each setting;Δ\\Deltais the AUROC margin\. “Rival” is the baseline with the largest Holm\-adjustedpp\-value in that row of Table[7](https://arxiv.org/html/2608.12592#A6.T7), i\.e\. the one whose margin is hardest to establish\. Only the saturated AI\-READI CGM\+\+Lab mode fails to separate\.
BaselineWinsMedianΔ\\DeltaWWppDiffusion\-TS8/8\+0\.137\+0\.137000\.00780\.0078ImagenTime8/8\+0\.142\+0\.142000\.00780\.0078VerbalTS8/8\+0\.165\+0\.165000\.00780\.0078Bridge8/8\+0\.157\+0\.157000\.00780\.0078TimeWeaver8/8\+0\.147\+0\.147000\.00780\.0078WaveStitch8/8\+0\.152\+0\.152000\.00780\.0078

Table 9:Exact two\-sided Wilcoxon signed\-rank test over the eight \(dataset, task\) settings, pairing ReCoGen’s AUROC with each baseline’s\. “Wins” counts settings with a positive difference\.p=0\.0078p\{=\}0\.0078is the smallest value attainable atn=8n\{=\}8, so it is reached whenever a method wins every setting; the test establishes consistency across settings, not the size of any single margin\.