FairDiffuseVQVAE: Sampling-Time Fairness in Tabular Diffusion via Conditional Refinement of Vector-Quantized Latents

# Sampling-Time Fairness in Tabular Diffusion via Conditional Refinement of Vector-Quantized Latents
Source: [https://arxiv.org/html/2607.28945](https://arxiv.org/html/2607.28945)
Mahdi Bagheri University of California, IrvineAmir M\. Rahmani University of California, Irvine

###### Abstract

Synthetic tabular data is increasingly used in privacy\-preserving data sharing, data augmentation, and to mitigate downstream classifier bias\. State\-of\-the\-art tabular diffusion models such as TabDDPM and TabSyn achieve excellent distributional fidelity but offer no mechanism for fairness; conversely, fairness\-aware tabular generators \(DECAF, FairTGAN, FairTabDDPM\) impose explicit fairness penalties at training time, yielding modest fairness gains at substantial cost to either sample quality or downstream utility\. We introduceFairDiffuseVQVAE, a two\-stage architecture that decouples fidelity from fairness: a vector\-quantized autoencoder with a row\-level discriminator \(Stage 1, no fairness terms\) is followed by a DiffuseVAE\-style continuous diffusion refiner that conditions on both the Stage\-1 reconstruction*and*the protected attribute via classifier\-free guidance \(Stage 2\)\. Fairness emerges as a property of the*sampling distribution*—uniform sampling of the protected attribute at inference time enforces demographic parity by construction—rather than from competing loss terms\. On theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)benchmark \(Adult, Bank, COMPAS\), FairDiffuseVQVAE achieves the highest mean Demographic Parity Ratio \(0\.7020\.702,\+47%\+47\\%over FairTabDDPM\) and Equalized Odds Ratio \(0\.6860\.686,\+100%\+100\\%\)\. It also attains the lowest mean pair\-wise correlation error \(0\.0340\.034\) of any published method, while explicitly trading∼\\sim1515AUC points for these fairness gains\.

## 1Introduction

Tabular data is the dominant modality in healthcare, finance, social science, and public policy\(Borisov et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib10)\)\. Releasing such data is constrained by privacy regulations \(HIPAA, GDPR\)\(Jordon et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib24)\), by the difficulty of obtaining representative samples for under\-represented populations, and—most critically—by the bias these datasets often encode\. A loan approval dataset that historically over\-represents one demographic group will train a downstream model that perpetuates that bias, even if the model itself is unbiased\(Caton and Haas,[2024](https://arxiv.org/html/2607.28945#bib.bib12); Plečko and Bareinboim,[2024](https://arxiv.org/html/2607.28945#bib.bib39)\)\. Synthetic tabular data generation promises to address all three issues simultaneously: produce realistic samples that obey privacy constraints, expand support across under\-represented groups, and reduce downstream classifier bias\.

Recent diffusion models for tabular data have closed most of the*quality*gap to real data\. TabDDPM\(Kotelnikov et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib29)\)adapts denoising diffusion to mixed\-type tabular features, and TabSyn\(Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55)\)pushes this further by performing diffusion in the latent space of a learned VAE, achieving sub\-1% column\-wise density error\. However, none of these methods offer any guarantee on the*fairness*of the generated data: the synthetic distribution inherits whatever statistical bias the training data contained\.

A complementary line of work explicitly targets fair tabular synthesis\. DECAF\(van Breugel et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib45)\)introduces causally\-aware fairness edits to a GAN; FairTGAN and FairTabDDPM\(Yang et al\.,[2025](https://arxiv.org/html/2607.28945#bib.bib54)\)add fairness penalty terms to a tabular GAN/DDPM respectively\. These methods improve fairness metrics but typically at the cost of sample quality \(FairTabDDPM density error0\.1190\.119vs TabSyn’s0\.0150\.015\) or downstream utility—a tension we observe sharpens when the underlying generative architecture is forced to balance reconstruction with adversarial or auxiliary losses\.

#### Our perspective\.

We argue that the fairness mechanism should not compete with reconstruction during training\. Instead, fairness can be enforced at*sampling time*if the generative model is conditioned on the protected attribute\. By drawing the protected attribute from a uniform distribution at sampling time, the marginal synthetic distribution satisfies demographic parity by construction; classifier\-free guidance\(Ho and Salimans,[2022](https://arxiv.org/html/2607.28945#bib.bib21)\)provides a tunable knob to control how strongly samples concentrate on the conditional manifold\. To make this practical for tabular data, we couple a vector\-quantized autoencoder \(Stage 1\) with a continuous diffusion refiner \(Stage 2\) trained in input space and conditioned on \(i\) the Stage\-1 reconstruction and \(ii\) the protected attribute\. The Stage\-1 model is trained without any fairness term; all fairness regularization is deferred to the conditional structure of Stage 2\.

#### Contributions\.

- •We introduceFairDiffuseVQVAE, a two\-stage architecture that combines a VQGAN\-style autoencoder\(Esser et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib17); van den Oord et al\.,[2017](https://arxiv.org/html/2607.28945#bib.bib46)\)with a DiffuseVAE\-style\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\)input\-space diffusion refiner\. The fairness mechanism is sampling\-time classifier\-free guidance over the protected attribute; no explicit fairness loss term is required\.
- •We demonstrate that this design beats fairness\-specific baselines by large margins on theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)benchmark: mean Demographic Parity Ratio of0\.7020\.702\(\+47%\+47\\%over FairTabDDPM\) and mean Equalized Odds Ratio of0\.6860\.686\(\+100%\+100\\%\)\.
- •We also show that the same architecture attains the lowest mean pair\-wise column correlation error \(0\.0340\.034\) of any published method, beating TabSyn \(0\.0410\.041\); the utility\-fairness trade\-off costs roughly1515AUC points relative to the strongest baselines\.
- •We provide a reproducible pipeline integrated into theTabSynrepository, supporting all eight datasets used across\(Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55); Yang et al\.,[2025](https://arxiv.org/html/2607.28945#bib.bib54)\)and reporting density, pair\-correlation, AUC, DCR, DPR, and EOR consistently\.

## 2Background

### 2\.1Vector Quantization and the VQGAN

A vector\-quantized variational autoencoder \(VQ\-VAE,van den Oord et al\.,[2017](https://arxiv.org/html/2607.28945#bib.bib46)\), built on the variational autoencoder foundation\(Kingma and Welling,[2014](https://arxiv.org/html/2607.28945#bib.bib28); Rezende et al\.,[2014](https://arxiv.org/html/2607.28945#bib.bib41)\), augments a standard autoencoder with a discrete codebook𝒵=\{ek\}k=1K\\mathcal\{Z\}=\\\{e\_\{k\}\\\}\_\{k=1\}^\{K\}of learned embedding vectors\. The encoder outputzez\_\{e\}is replaced by its nearest codebook entryzqz\_\{q\}, and gradients propagate through the quantization step via the straight\-through estimator\(Bengio et al\.,[2013](https://arxiv.org/html/2607.28945#bib.bib8)\)\. The codebook plus a commitment loss \(β​‖ze−sg​\[zq\]‖2\\beta\\\|z\_\{e\}\-\\mathrm\{sg\}\[z\_\{q\}\]\\\|^\{2\}\) regularize the latent space\. VQGAN\(Esser et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib17)\)extends VQ\-VAE with a perceptual loss\(Zhang et al\.,[2018](https://arxiv.org/html/2607.28945#bib.bib56)\)and a patch\-level discriminator\(Goodfellow et al\.,[2014](https://arxiv.org/html/2607.28945#bib.bib18)\), producing high\-fidelity image reconstructions that admit downstream generative modelling \(typically by an autoregressive prior over codebook indices\)\.

### 2\.2Diffusion Models and EDM

Denoising diffusion probabilistic models \(DDPMs,Ho et al\.,[2020](https://arxiv.org/html/2607.28945#bib.bib22)\) generate samples by reversing a Markov chain that gradually adds Gaussian noise\. We adopt theKarras et al\. \([2022](https://arxiv.org/html/2607.28945#bib.bib25)\)\(EDM\) formulation, which expresses the forward process by a continuous noise levelσ\\sigmadrawn from a log\-normal distribution and trains a denoiserDθD\_\{\\theta\}with the weighted MSE objective𝔼σ,ϵ,x​\[w​\(σ\)​‖Dθ​\(x\+σ​ϵ,σ\)−x‖2\]\\mathbb\{E\}\_\{\\sigma,\\epsilon,x\}\\big\[w\(\\sigma\)\\\|D\_\{\\theta\}\(x\+\\sigma\\epsilon,\\sigma\)\-x\\\|^\{2\}\\big\], wherew​\(σ\)=\(σ2\+σdata2\)/\(σ​σdata\)2w\(\\sigma\)=\(\\sigma^\{2\}\+\\sigma\_\{\\mathrm\{data\}\}^\{2\}\)/\(\\sigma\\sigma\_\{\\mathrm\{data\}\}\)^\{2\}\. EDM samplers \(Heun\) require fewer function evaluations than vanilla DDPM at comparable sample quality\. Latent diffusion models \(LDM,Rombach et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib42)\) compose a VAE with an EDM/DDPM in the*latent*space; DiffuseVAE\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\)composes them differently—a DDPM in*input*space conditioned on the VAE’s reconstruction\.

### 2\.3Classifier\-Free Guidance

Classifier\-free guidance \(CFG,Ho and Salimans,[2022](https://arxiv.org/html/2607.28945#bib.bib21)\) trains a single denoiser jointly on conditional and unconditional examples \(by stochastically dropping the conditioning signal during training\), then at sampling time interpolates the two predictions:D^cfg=D∅\+w​\(Dc−D∅\)\\hat\{D\}^\{\\mathrm\{cfg\}\}=D^\{\\varnothing\}\+w\(D^\{c\}\-D^\{\\varnothing\}\)\. Forw\>1w\>1, samples are pushed further into the conditional manifold; forw=1w=1, behaviour matches standard conditional sampling\.

### 2\.4Fairness Metrics

FollowingYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\), who followAgarwal et al\. \([2018](https://arxiv.org/html/2607.28945#bib.bib2)\); Hardt et al\. \([2016](https://arxiv.org/html/2607.28945#bib.bib20)\), we useDemographic Parity Ratio \(DPR\)andEqualized Odds Ratio \(EOR\), both in\[0,1\]\[0,1\]with11denoting perfect parity\. LetY^\\hat\{Y\}be a downstream classifier trained on synthetic data and evaluated on real data with sensitive attributeAA:

DPR\\displaystyle\\mathrm\{DPR\}=mina⁡Pr⁡\(Y^=1∣A=a\)maxa⁡Pr⁡\(Y^=1∣A=a\),\\displaystyle=\\frac\{\\min\_\{a\}\\Pr\(\\hat\{Y\}=1\\mid A=a\)\}\{\\max\_\{a\}\\Pr\(\\hat\{Y\}=1\\mid A=a\)\},\(1\)EOR\\displaystyle\\mathrm\{EOR\}=min⁡\(mina⁡TPRamaxa⁡TPRa,mina⁡FPRamaxa⁡FPRa\)\.\\displaystyle=\\min\\left\(\\frac\{\\min\_\{a\}\\mathrm\{TPR\}\_\{a\}\}\{\\max\_\{a\}\\mathrm\{TPR\}\_\{a\}\},\\,\\frac\{\\min\_\{a\}\\mathrm\{FPR\}\_\{a\}\}\{\\max\_\{a\}\\mathrm\{FPR\}\_\{a\}\}\\right\)\.\(2\)DPR captures equal allocation; EOR captures equal performance\.

## 3Related Work

#### Tabular data synthesis\.

Early work used GANs \(CTGAN and TVAE,Xu et al\.,[2019](https://arxiv.org/html/2607.28945#bib.bib53); CTAB\-GAN\+,Zhao et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib57)\) and copula methods\. More recent diffusion\-based methods include TabDDPM\(Kotelnikov et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib29)\), which applies categorical and Gaussian diffusion in input space; STaSy\(Kim et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib27)\), which uses score\-based generative modelling; CoDi\(Lee et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib33)\), which contrasts sub\-tables; and TabSyn\(Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55)\), which performs EDM diffusion in the latent space of a learned tabular VAE and is the current state of the art on column\-wise density estimation\. GReaT\(Borisov et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib11)\)treats tabular rows as text and fine\-tunes a language model; GOGGLE\(Liu et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib34)\)learns a graph structure over columns\. None of these methods address fairness explicitly\.

#### Fairness in tabular synthesis\.

Early fair tabular GANs include FairGAN\(Xu et al\.,[2018](https://arxiv.org/html/2607.28945#bib.bib52)\)and TabFairGAN\(Rajabi and Garibay,[2022](https://arxiv.org/html/2607.28945#bib.bib40)\), which add adversarial fairness losses to a tabular GAN\. DECAF\(van Breugel et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib45)\)fits a causal DAG over the columns and re\-weights or removes edges to enforce one of three fairness notions \(Fairness Through Unawareness, Demographic Parity, Counterfactual Fairness\) at sampling time\.Abroshan et al\. \([2024](https://arxiv.org/html/2607.28945#bib.bib1)\)impose post\-hoc fairness constraints on synthetic data via re\-sampling, and CuTS\(Vero et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib48)\)learns a customisable bias\-aware tabular generator\. TabFairGDT\(Panagiotou et al\.,[2025](https://arxiv.org/html/2607.28945#bib.bib37)\)uses autoregressive decision trees for fast fair generation\. FairTGAN and FairTabDDPM\(Yang et al\.,[2025](https://arxiv.org/html/2607.28945#bib.bib54)\)—the closest prior work to ours—add fairness penalties to a tabular GAN and a tabular DDPM respectively, achieving moderate fairness improvements at the cost of density\-estimation quality \([Table2](https://arxiv.org/html/2607.28945#S6.T2)\)\. Our work differs in three important ways: \(i\) we use a two\-stage architecture where the autoencoder is trained without any fairness term, isolating fidelity from fairness; \(ii\) we enforce fairness at sampling time via classifier\-free guidance, providing a tunable knob rather than a fixed penalty; \(iii\) we operate the diffusion refiner in input space conditioned on the Stage\-1 reconstruction, following the DiffuseVAE recipe\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\)but with a quantized autoencoder\. As[Section6](https://arxiv.org/html/2607.28945#S6)shows, this combination beats all published baselines on DPR and EOR\.

#### Generative fairness more broadly\.

The Variational Fair Autoencoder\(Louizos et al\.,[2016](https://arxiv.org/html/2607.28945#bib.bib35)\)pioneered information\-theoretic fairness via Maximum Mean Discrepancy\(Gretton et al\.,[2012](https://arxiv.org/html/2607.28945#bib.bib19)\)on the latent space\. Many follow\-ups\(Madras et al\.,[2018](https://arxiv.org/html/2607.28945#bib.bib36); Creager et al\.,[2019](https://arxiv.org/html/2607.28945#bib.bib14)\)use adversarial debiasing or disentanglement\-style losses\. Beyond representation\-level approaches, the broader fair\-ML landscape is surveyed byCaton and Haas \([2024](https://arxiv.org/html/2607.28945#bib.bib12)\)andWan et al\. \([2023](https://arxiv.org/html/2607.28945#bib.bib49)\);Plečko and Bareinboim \([2024](https://arxiv.org/html/2607.28945#bib.bib39)\)provide a causal\-inference perspective; andLe Quy et al\. \([2022](https://arxiv.org/html/2607.28945#bib.bib32)\)catalogue fairness datasets\. Path\-specific counterfactual fairness\(Chiappa,[2019](https://arxiv.org/html/2607.28945#bib.bib13)\)and the broader counterfactual framework\(Kusner et al\.,[2017](https://arxiv.org/html/2607.28945#bib.bib30)\)provide alternative formalisms\. We initially explored an in\-training fairness direction \(MMD onzez\_\{e\}plus a correlation penalty on the decoder output\) but found it consistently traded off quality for negligible fairness gains in our two\-stage setting; the conditional\-sampling mechanism we adopt here was both simpler and more effective\.

#### Discrete diffusion as an alternative\.

An alternative to our quantize\-then\-refine approach is to perform diffusion directly in a discrete state space\. D3PM\(Austin et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib5)\)extends DDPM with categorical transition kernels; TabDDPM\(Kotelnikov et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib29)\)uses a related multinomial\-diffusion process for the categorical columns of tabular data\. We chose continuous diffusion in the rich \(one\-hot\) representation followed by argmax decoding for two reasons: \(i\) it admits the standard EDM toolkit unchanged, including classifier\-free guidance; \(ii\) Stage 1’s autoencoder already learns a smooth latent geometry that the diffusion refiner can condition on in input space\.

#### Vector\-quantized generative models\.

Beyond images, VQ\-VAEs have been applied widely; the closest tabular precedents combine VQ with downstream generative priors\. To our knowledge, this is the first application of VQGAN\-style vector quantization combined with input\-space DiffuseVAE refinement\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\)to fair tabular synthesis\.

#### Evaluation methodology\.

We follow established sample\-quality protocols: column\-shape and column\-pair\-trend scores from SDMetrics\(DataCebo, Inc\.,[2023](https://arxiv.org/html/2607.28945#bib.bib15)\), manifold precision/recall at the sample level\(Sajjadi et al\.,[2018](https://arxiv.org/html/2607.28945#bib.bib43); Alaa et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib3)\), and the TSTR \(train on synthetic, test on real\) protocol popularized by PATE\-GAN\(Jordon et al\.,[2019](https://arxiv.org/html/2607.28945#bib.bib23)\)\.

## 4Method: FairDiffuseVQVAE

x¯\\bar\{x\}EncoderEϕE\_\{\\phi\}zez\_\{e\}VQzqz\_\{q\}DecoderGθG\_\{\\theta\}x¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}Codebook𝒵\\mathcal\{Z\}\{ek\}k=1K\\\{e\_\{k\}\\\}\_\{k=1\}^\{K\}protectedssDiscriminatorDξD\_\{\\xi\}ℒrecon\\mathcal\{L\}\_\{\\mathrm\{recon\}\}\(MSE \+ CE\)ℒcodebook,ℒcommit\\mathcal\{L\}\_\{\\mathrm\{codebook\}\},\\;\\mathcal\{L\}\_\{\\mathrm\{commit\}\}ℒGAN\\mathcal\{L\}\_\{\\mathrm\{GAN\}\}nearest\-nb\. lookupconditionfakerealx¯\\bar\{x\}\(EϕE\_\{\\phi\}does not seess\)x¯\\bar\{x\}\+\+x¯t\\bar\{x\}\_\{t\}Conditional denoiserDψD\_\{\\psi\}5\-layer MLP, 512\-d, EDMx¯^\\hat\{\\bar\{x\}\}σ∼LogNormal​\(Pmean,Pstd2\)\\sigma\\sim\\mathrm\{LogNormal\}\(P\_\{\\mathrm\{mean\}\},P\_\{\\mathrm\{std\}\}^\{2\}\)ss/∅\\varnothingℒStage2\\mathcal\{L\}\_\{\\mathrm\{Stage2\}\}x¯\+σ​ϵ\\bar\{x\}\+\\sigma\\epsilonϵ∼𝒩​\(0,I\)\\epsilon\\sim\\mathcal\{N\}\(0,I\)σ\\sigmaclassifier\-free guidancedropssw\.p\.pcfg=0\.3p\_\{\\mathrm\{cfg\}\}\{=\}0\.3x¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}: frozen Stage\-1 reconstruction\(conditioning input\)Draws∼Bernoulli​\(0\.5\)s\\sim\\mathrm\{Bernoulli\}\(0\.5\)\(uniform protected attr\.\)Draw random codes\{ki\}i=1n∼Unif\\\{k\_\{i\}\\\}\_\{i=1\}^\{n\}\\sim\\mathrm\{Unif\}DecodeGθ​\(\{eki\},s\)G\_\{\\theta\}\(\\\{e\_\{k\_\{i\}\}\\\},s\)=x¯^VQ\(0\)=\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}^\{\(0\)\}Heun EDM refiner50 steps, CFGwcfgw\_\{\\mathrm\{cfg\}\}Synthetic row\(x¯,s\)\(\\bar\{x\},s\)demographic parityssalso conditions the refinerStage 1 — Fair Vector\-Quantized AutoencoderStage 2 — Fair Refinement via Conditional Input\-Space DiffusionSampling — Demographic\-Parity Generation

Figure 1:Overview ofFairDiffuseVQVAE\.A two\-stage architecture for fair mixed\-type tabular synthesis\.Stage 1trains a vector\-quantized autoencoder: an encoderEϕE\_\{\\phi\}maps a rowx¯\\bar\{x\}to latent tokenszez\_\{e\}, which are quantized against a learned codebook𝒵\\mathcal\{Z\}and decoded byGθG\_\{\\theta\}into a reconstructionx¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}, with a row\-level discriminatorDξD\_\{\\xi\}providing an adversarial signal\. The decoder is conditioned on the protected attributesswhile the encoder is not, and Stage 1 carries no explicit fairness term\.Stage 2trains a conditional EDM denoiserDψD\_\{\\psi\}that refines the \(frozen\) Stage\-1 reconstruction in input space:x¯\\bar\{x\}is perturbed tox¯t\\bar\{x\}\_\{t\}at noise scaleσ\\sigma, andDψD\_\{\\psi\}is conditioned onx¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}, onσ\\sigma, and onsswith classifier\-free\-guidance dropout \(pcfgp\_\{\\mathrm\{cfg\}\}\)\.Samplingdrawss∼Bernoulli​\(0\.5\)s\\sim\\mathrm\{Bernoulli\}\(0\.5\), decodes random codebook indices into an initial guess, and refines it with a 50\-step Heun EDM sampler\. Becausessis drawn uniformly whileDψD\_\{\\psi\}modelsp​\(x¯∣s\)p\(\\bar\{x\}\\mid s\), the synthetic distribution satisfies demographic parity by construction\. Dashed teal arrows denote conditioning onss; red italic labels mark training losses\.We proposeFairDiffuseVQVAE, a two\-stage tabular synthesis architecture that combines a vector\-quantized autoencoder with a conditional denoising diffusion refiner\. Fairness is enforced not by adding penalty terms during training, but as a property of the conditional generative process at sampling time, via classifier\-free guidance over the protected attribute\.

### 4\.1Notation and Setup

Letx∈ℝdc×\{0,1\}ddx\\in\\mathbb\{R\}^\{d\_\{c\}\}\\times\\\{0,1\\\}^\{d\_\{d\}\}denote a mixed\-type tabular row withdcd\_\{c\}continuous andddd\_\{d\}categorical features,s∈\{0,1\}s\\in\\\{0,1\\\}the binary protected attribute, andy∈\{0,1\}y\\in\\\{0,1\\\}the outcome label\. Categorical columns are encoded one\-hot; we writex¯∈ℝD\\bar\{x\}\\in\\mathbb\{R\}^\{D\}for the resulting concatenated representation of dimensionD=dc\+∑jKjD=d\_\{c\}\+\\sum\_\{j\}K\_\{j\}whereKjK\_\{j\}is the cardinality of thejj\-th categorical column\.

#### Overview\.

[Figure1](https://arxiv.org/html/2607.28945#S4.F1)summarizesFairDiffuseVQVAE\. The central design choice is to decouple*fidelity*from*fairness*: Stage 1 is responsible only for learning a faithful, compact representation of mixed\-type rows, while Stage 2 and the sampling procedure are responsible for fairness\. Neither stage optimizes a fairness penalty during training\. Instead, fairness emerges at sampling time—the diffusion refiner is trained as a conditional modelp​\(x¯∣s\)p\(\\bar\{x\}\\mid s\)with classifier\-free guidance, so drawingssfrom a uniform prior rather than the \(typically biased\) data marginal yields a synthetic jointpsynth​\(x¯,s\)=Unif​\(s\)​p​\(x¯∣s\)p\_\{\\mathrm\{synth\}\}\(\\bar\{x\},s\)=\\mathrm\{Unif\}\(s\)\\,p\(\\bar\{x\}\\mid s\)that satisfies demographic parity by construction\. This separation lets the guidance scalewcfgw\_\{\\mathrm\{cfg\}\}serve as a single, interpretable knob that trades conditional concentration against utility, with no retraining\. The remainder of this section details the two stages \([Sections4\.2](https://arxiv.org/html/2607.28945#S4.SS2)and[4\.3](https://arxiv.org/html/2607.28945#S4.SS3)\) and the sampling procedure \([Section4\.3](https://arxiv.org/html/2607.28945#S4.SS3)\)\.

### 4\.2Stage 1: Fair Vector\-Quantized Autoencoder

#### Architecture\.

The Stage 1 model is a VQGAN\(Esser et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib17)\)adapted to mixed\-type tabular data\. The encoderEϕ​\(x¯\)=ze∈ℝn⋅dzE\_\{\\phi\}\(\\bar\{x\}\)=z\_\{e\}\\in\\mathbb\{R\}^\{n\\cdot d\_\{z\}\}is a fully\-connected network producingnnpre\-quantization latent tokens, each of dimensiondzd\_\{z\}\. A learned codebook𝒵=\{ek∈ℝdz\}k=1K\\mathcal\{Z\}=\\\{e\_\{k\}\\in\\mathbb\{R\}^\{d\_\{z\}\}\\\}\_\{k=1\}^\{K\}quantizes each token by nearest\-neighbor lookup,

zq\(i\)=eki∗,ki∗=arg⁡mink∈\{1,…,K\}⁡‖ze\(i\)−ek‖22\.z\_\{q\}^\{\(i\)\}=e\_\{k^\{\\ast\}\_\{i\}\},\\quad k^\{\\ast\}\_\{i\}=\\arg\\min\_\{k\\in\\\{1,\\ldots,K\\\}\}\\\|z\_\{e\}^\{\(i\)\}\-e\_\{k\}\\\|\_\{2\}^\{2\}\.\(3\)The decoderGθ​\(zq,s\)=x¯^G\_\{\\theta\}\(z\_\{q\},s\)=\\hat\{\\bar\{x\}\}reconstructs the row from the quantized latents conditioned on the protected attributess, and a row\-level discriminatorDξD\_\{\\xi\}distinguishes real and reconstructed rows\. The encoderEϕE\_\{\\phi\}does not receivessas input\.

#### Mixed\-type reconstruction\.

The decoder emits per\-column heads: a scalar for each continuous column and aKjK\_\{j\}\-dimensional logit vector for each categorical column\. The reconstruction loss combines mean\-squared error on continuous columns with cross\-entropy on categorical columns:

ℒrecon=1dc​∑j∈𝒞contMSE​\(x^j,xj\)\+1dd​∑j∈𝒞catCE​\(ℓ^j,xj\),\\mathcal\{L\}\_\{\\mathrm\{recon\}\}\\;=\\;\\frac\{1\}\{d\_\{c\}\}\\sum\_\{j\\in\\mathcal\{C\}\_\{\\mathrm\{cont\}\}\}\\mathrm\{MSE\}\(\\hat\{x\}\_\{j\},x\_\{j\}\)\+\\frac\{1\}\{d\_\{d\}\}\\sum\_\{j\\in\\mathcal\{C\}\_\{\\mathrm\{cat\}\}\}\\mathrm\{CE\}\(\\hat\{\\ell\}\_\{j\},x\_\{j\}\),\(4\)whereℓ^j∈ℝKj\\hat\{\\ell\}\_\{j\}\\in\\mathbb\{R\}^\{K\_\{j\}\}are the predicted logits for columnjj\. This replaces the pure MSE\-on\-integer\-codes formulation used in earlier tabular VAEs and substantially improves column\-wise distribution fidelity\.

#### Codebook and adversarial losses\.

We use the standard VQ\-VAE codebook and commitment losses\(van den Oord et al\.,[2017](https://arxiv.org/html/2607.28945#bib.bib46)\):

ℒcodebook\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{codebook\}\}=‖sg​\[ze\]−zq‖22,\\displaystyle=\\\|\\mathrm\{sg\}\[z\_\{e\}\]\-z\_\{q\}\\\|\_\{2\}^\{2\},\(5\)ℒcommit\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{commit\}\}=‖ze−sg​\[zq\]‖22,\\displaystyle=\\\|z\_\{e\}\-\\mathrm\{sg\}\[z\_\{q\}\]\\\|\_\{2\}^\{2\},\(6\)wheresg​\[⋅\]\\mathrm\{sg\}\[\\cdot\]denotes the stop\-gradient operator\. Gradients through the quantization step are propagated by the straight\-through estimator\. The adversarial objective is the standard non\-saturating GAN loss with the autoencoder\(Eϕ,Gθ\)\(E\_\{\\phi\},G\_\{\\theta\}\)as generator andDξD\_\{\\xi\}as discriminator\.

#### Stage 1 objective\.

The total generator\-side loss is

ℒStage1gen=ℒrecon\+ℒcodebook\+β​ℒcommit\+λadv​ℒGAN,\\mathcal\{L\}^\{\\mathrm\{gen\}\}\_\{\\mathrm\{Stage1\}\}=\\mathcal\{L\}\_\{\\mathrm\{recon\}\}\+\\mathcal\{L\}\_\{\\mathrm\{codebook\}\}\+\\beta\\,\\mathcal\{L\}\_\{\\mathrm\{commit\}\}\+\\lambda\_\{\\mathrm\{adv\}\}\\,\\mathcal\{L\}\_\{\\mathrm\{GAN\}\},\(7\)withβ=0\.25\\beta=0\.25followingvan den Oord et al\. \([2017](https://arxiv.org/html/2607.28945#bib.bib46)\)andλadv=0\.1\\lambda\_\{\\mathrm\{adv\}\}=0\.1\. The discriminator is updated with the standard adversarial objective, gated by a 60\-epoch warm\-up during which only the reconstructive losses are active\.*Stage 1 does not include any explicit fairness term\.*

### 4\.3Stage 2: Fair Refinement via Conditional Input\-Space Diffusion

#### Motivation\.

A trained Stage 1 model produces a reconstructionx¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}for any row, but generation requires sampling the codebook\. Rather than fitting an autoregressive prior over discrete codes\(van den Oord et al\.,[2017](https://arxiv.org/html/2607.28945#bib.bib46); Esser et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib17)\), we adopt the DiffuseVAE\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\)recipe, refining a Stage\-1 reconstruction with a DDPM in input space and conditioning explicitly on the protected attributess\. Fairness is then a property of the sampling distribution rather than an explicit loss term\.

#### Input\-space diffusion refiner\.

We train a denoiserDψ​\(x¯t,σ;x¯^VQ,s\)D\_\{\\psi\}\(\\bar\{x\}\_\{t\},\\sigma;\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\},s\)directly on the one\-hot input representationx¯∈ℝD\\bar\{x\}\\in\\mathbb\{R\}^\{D\}, conditioned on the frozen Stage\-1 reconstructionx¯^VQ=Gθ​\(zq,s\)\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}=G\_\{\\theta\}\(z\_\{q\},s\)\. The denoiser is trained under the EDM\(Karras et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib25)\)formulation:

σ\\displaystyle\\sigma∼LogNormal​\(Pmean,Pstd2\),\\displaystyle\\sim\\mathrm\{LogNormal\}\(P\_\{\\mathrm\{mean\}\},P\_\{\\mathrm\{std\}\}^\{2\}\),\(8\)x¯t\\displaystyle\\bar\{x\}\_\{t\}=x¯\+σ⋅ϵ,ϵ∼𝒩​\(0,I\),\\displaystyle=\\bar\{x\}\+\\sigma\\cdot\\epsilon,\\quad\\epsilon\\sim\\mathcal\{N\}\(0,I\),\(9\)ℒStage2\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{Stage2\}\}=𝔼​\[w​\(σ\)​‖Dψ​\(x¯t,σ;x¯^VQ,s\)−x¯‖22\],\\displaystyle=\\mathbb\{E\}\\bigl\[w\(\\sigma\)\\,\\\|D\_\{\\psi\}\(\\bar\{x\}\_\{t\},\\sigma;\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\},s\)\-\\bar\{x\}\\\|\_\{2\}^\{2\}\\bigr\],\(10\)withw​\(σ\)=\(σ2\+σdata2\)/\(σ​σdata\)2w\(\\sigma\)=\(\\sigma^\{2\}\+\\sigma\_\{\\mathrm\{data\}\}^\{2\}\)/\(\\sigma\\sigma\_\{\\mathrm\{data\}\}\)^\{2\},Pmean=−1\.2P\_\{\\mathrm\{mean\}\}=\-1\.2,Pstd=1\.2P\_\{\\mathrm\{std\}\}=1\.2,σdata=0\.5\\sigma\_\{\\mathrm\{data\}\}=0\.5\. This places FairDiffuseVQVAE in the family of DiffuseVAE\-style input\-space refiners\(Pandey et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib38)\), distinct from latent\-diffusion generators that denoise in a learned latent space\(Rombach et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib42); Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55)\)\.x¯^VQ\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}is concatenated to the denoiser’s input alongside the sinusoidal embedding ofσ\\sigma, andssis injected through a learned conditioning embedding\. The denoiserDψD\_\{\\psi\}is a 5\-layer MLP with 512\-dim hidden width\.

#### Classifier\-free guidance\.

We train with classifier\-free guidance\(Ho and Salimans,[2022](https://arxiv.org/html/2607.28945#bib.bib21)\): with probabilitypcfg=0\.3p\_\{\\mathrm\{cfg\}\}=0\.3,ssis replaced by a learned null token during training\. At sampling time, the conditional and unconditional predictions are combined as

Dψcfg​\(x¯t,σ;x¯^VQ,s\)=Dψ∅\+wcfg⋅\(Dψs−Dψ∅\),D\_\{\\psi\}^\{\\mathrm\{cfg\}\}\(\\bar\{x\}\_\{t\},\\sigma;\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\},s\)=D\_\{\\psi\}^\{\\varnothing\}\+w\_\{\\mathrm\{cfg\}\}\\cdot\(D\_\{\\psi\}^\{s\}\-D\_\{\\psi\}^\{\\varnothing\}\),\(11\)with guidance strengthwcfg≥1w\_\{\\mathrm\{cfg\}\}\\geq 1\. This single mechanism both enables conditional generation and provides a tunable fairness knob\.

#### Sampling\.

Generation proceeds in three steps: \(i\) draws∼Bernoulli​\(0\.5\)s\\sim\\mathrm\{Bernoulli\}\(0\.5\)to enforce demographic\-parity sampling; \(ii\) draw random codebook indices\{ki\}i=1n\\\{k\_\{i\}\\\}\_\{i=1\}^\{n\}uniformly and decode them to an initial guessx¯^VQ\(0\)=Gθ​\(\{eki\},s\)\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}^\{\(0\)\}=G\_\{\\theta\}\(\\\{e\_\{k\_\{i\}\}\\\},s\); \(iii\) refine via 50 steps of Heun’s second\-order EDM sampler conditioned on\(x¯^VQ\(0\),s\)\(\\hat\{\\bar\{x\}\}\_\{\\mathrm\{VQ\}\}^\{\(0\)\},s\)\. Categorical columns are recovered from the refined output by argmax over the per\-column logit slices; continuous columns are inverse\-standardised\.

#### Why this enforces fairness\.

At sampling time,ssis drawn from a uniform distribution rather than the \(typically biased\) data marginal\. Because the denoiser is trained asp​\(x¯∣s\)p\(\\bar\{x\}\\mid s\)with classifier\-free guidance dropout, the marginal synthetic distributionpsynth​\(x¯,s\)=Unif​\(s\)⋅p​\(x¯∣s\)p\_\{\\mathrm\{synth\}\}\(\\bar\{x\},s\)=\\mathrm\{Unif\}\(s\)\\cdot p\(\\bar\{x\}\\mid s\)satisfies demographic parity by construction: for any downstream binary predictorgg, the demographic\-parity gap reduces to\|𝔼p\(⋅\|0\)​\[g\]−𝔼p\(⋅\|1\)​\[g\]\|\|\\mathbb\{E\}\_\{p\(\\cdot\|0\)\}\[g\]\-\\mathbb\{E\}\_\{p\(\\cdot\|1\)\}\[g\]\|, which shrinks as the conditional distributionsp​\(x¯∣s=0\)p\(\\bar\{x\}\\mid s\{=\}0\)andp​\(x¯∣s=1\)p\(\\bar\{x\}\\mid s\{=\}1\)are pulled closer together by the guidance mechanism\. The guidance scalewcfgw\_\{\\mathrm\{cfg\}\}trades off conditional concentration against utility preservation\. We usewcfg=1w\_\{\\mathrm\{cfg\}\}=1throughout unless otherwise noted\.

## 5Experiments

### 5\.1Datasets

We evaluate FairDiffuseVQVAE on two complementary benchmarks: the six datasets used by TabSyn\(Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55)\)for general tabular synthesis quality, and the three datasets used by fair\-tab\-diffusion\(Yang et al\.,[2025](https://arxiv.org/html/2607.28945#bib.bib54)\)for fair tabular synthesis\. Three datasets \(Adult, Default\) overlap; the union is eight datasets covering∼\\sim5,000 to∼\\sim45,000 rows\.

Adult is the canonical UCI income\-prediction dataset\(Becker and Kohavi,[1996](https://arxiv.org/html/2607.28945#bib.bib6)\); Default and Bank are UCI clinical and marketing datasets respectively; COMPAS is the ProPublica recidivism dataset\(Angwin et al\.,[2016](https://arxiv.org/html/2607.28945#bib.bib4)\); Shoppers, Magic, Beijing, and News follow theZhang et al\. \([2024](https://arxiv.org/html/2607.28945#bib.bib55)\)benchmark protocol\. For each dataset we use the 80/10/10 train/val/test split\. Synthetic data is generated with the same number of rows as the training split\. Continuous columns are standard\-scaled; categorical columns are integer encoded by the data adapter and one\-hot expanded internally before being passed to the encoder\. For Bank, the age column is binarised at age<25<25to match the binarisation used byYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)\.

### 5\.2Baselines

We compare against the union of baselines reported by both reference papers\. FromZhang et al\. \([2024](https://arxiv.org/html/2607.28945#bib.bib55)\):SMOTE,CTGAN,TVAE,GOGGLE,GReaT,STaSy,CoDi,TabDDPM, andTabSynitself\. FromYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\): in addition to the above, the fairness\-awareFairCB\(Fair Class Balancing\) andFairTGAN\(fair tabular GAN\), as well as theirFairTabDDPMcontribution\. We report all baseline numbers as published; our model is denotedOursand is run with three random seeds for the fairness benchmark\. Note that SMOTE and FairCB are resampling/interpolation techniques rather than deep generative models, and are reported for context alongside, rather than as directly comparable competitors to, the deep generative baselines\.

### 5\.3Metrics

We report six metrics, mirroring theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)evaluation protocol exactly:

- •Density error↓\\downarrow:1−shape score1\-\\text\{shape score\}from SDMetrics\(DataCebo, Inc\.,[2023](https://arxiv.org/html/2607.28945#bib.bib15)\), the column\-wise marginal similarity\.
- •Pair\-correlation error↓\\downarrow:1−trend score1\-\\text\{trend score\}from SDMetrics, the pairwise correlation similarity\.
- •AUC↑\\uparrow: Train on Synthetic, Test on Real \(TSTR\) classifier accuracy\. FollowingYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\), we report the best of two classifiers \(logistic regression and a 100\-unit MLP\)\.
- •DCR\(∼0\.5\\sim 0\.5\):*Distance to Closest Record*\(Zhang et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib55)\), the fraction of synthetic samples nearer to a training row than to a held\-out test row\. Values close to0\.50\.5indicate no memorization\.
- •DPR↑\\uparrow:*Demographic Parity Ratio*\(Weerts et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib50)\),mina⁡P​\(Y^=1∣A=a\)/maxa⁡P​\(Y^=1∣A=a\)\\min\_\{a\}P\(\\hat\{Y\}=1\\mid A=a\)/\\max\_\{a\}P\(\\hat\{Y\}=1\\mid A=a\)\.
- •EOR↑\\uparrow:*Equalized Odds Ratio*\(Weerts et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib50)\), the smaller of the TPR and FPR ratios across sensitive groups\.

DPR and EOR are computed only on datasets with an annotated sensitive attribute \(Adult, Bank, COMPAS\); on the four TabSyn\-only datasets \(Shoppers, Magic, Beijing, News\) we report quality, utility, and privacy metrics\. We additionally report manifold precision/recall\(Sajjadi et al\.,[2018](https://arxiv.org/html/2607.28945#bib.bib43); Alaa et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib3); Kynkäänniemi et al\.,[2019](https://arxiv.org/html/2607.28945#bib.bib31)\)as a secondary fidelity check\.

### 5\.4Implementation Details

#### Stage 1\.

Encoder/decoder hidden width 256,n=8n=8tokens ofdz=32d\_\{z\}=32each, codebook sizeK=1024K=1024, batch size 256, 80 epochs with a 60\-epoch GAN warm\-up, Adam\(β1=0\.5,β2=0\.9\)\(\\beta\_\{1\}=0\.5,\\beta\_\{2\}=0\.9\)at lr10−310^\{\-3\}\.

#### Stage 2\.

5\-layer MLP denoiser of base width 512, EDM preconditioning withσdata=0\.5\\sigma\_\{\\mathrm\{data\}\}=0\.5, lognormalσ\\sigma\-sampling at\(Pmean,Pstd\)=\(−1\.2,1\.2\)\(P\_\{\\mathrm\{mean\}\},P\_\{\\mathrm\{std\}\}\)=\(\-1\.2,1\.2\)\. Trained for up to 400 epochs with early stopping \(patience 30 on a 10% validation split\), batch size 256, classifier\-free guidance dropoutpcfg=0\.3p\_\{\\mathrm\{cfg\}\}=0\.3\. Sampling uses 50 Heun steps withσmin=0\.002\\sigma\_\{\\mathrm\{min\}\}=0\.002,σmax=80\\sigma\_\{\\mathrm\{max\}\}=80,ρ=7\\rho=7, guidancewcfg=1w\_\{\\mathrm\{cfg\}\}=1\.

#### Compute\.

All models trained on a single Quadro RTX 5000\. End\-to\-end training and sampling take∼\\sim15–30 min per dataset, depending on size\.

## 6Results

### 6\.1Headline: Fair Tabular Synthesis Benchmark

[Table1](https://arxiv.org/html/2607.28945#S6.T1)reports DPR and EOR on theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)fairness benchmark\. FairDiffuseVQVAE achieves the highest mean DPR \(0\.7020\.702\) and EOR \(0\.6860\.686\) of all methods, surpassing the strongest fairness\-aware baseline FairTabDDPM by\+𝟒𝟕%\\mathbf\{\+47\\%\}and\+𝟏𝟎𝟎%\\mathbf\{\+100\\%\}respectively\. The gain is driven by Bank and COMPAS, where the demographic\-parity sampling mechanism substantially decouples the protected attribute from the synthesised features\.

DPR\(↑\\uparrow\)EOR\(↑\\uparrow\)MethodAdultBankCOMPASMeanAdultBankCOMPASMeanReal0\.3090\.4020\.6750\.4620\.1930\.3670\.6450\.402CoDi0\.2930\.1890\.8550\.4460\.2470\.1720\.8570\.425GReaT0\.2490\.5720\.6240\.4820\.1550\.3800\.5430\.359SMOTE0\.3210\.4050\.6480\.4580\.2540\.3810\.5890\.408STaSy0\.2610\.4680\.4360\.3880\.1820\.4510\.4330\.355TabDDPM0\.2610\.3370\.5580\.3850\.1560\.3340\.5400\.343TabSyn0\.2810\.3360\.6970\.4380\.1780\.3170\.6640\.386FairCB0\.2860\.7190\.6750\.5600\.1920\.8010\.6380\.544FairTGAN0\.5540\.3380\.4480\.4470\.6970\.1580\.3920\.416FairTabDDPM0\.5430\.3370\.5580\.4790\.1560\.3340\.5400\.343Ours0\.5330\.6870\.8850\.7020\.5940\.6970\.7670\.686

Table 1:Demographic Parity Ratio \(DPR\) and Equalized Odds Ratio \(EOR\) on theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)benchmark\. All values are means over three random seeds; standard deviations are reported in[Table4](https://arxiv.org/html/2607.28945#S6.T4)\.Oursachieves the highest mean on both metrics,\+𝟒𝟕%\\mathbf\{\+47\\%\}over FairTabDDPM on DPR and\+𝟏𝟎𝟎%\\mathbf\{\+100\\%\}on EOR\.
### 6\.2Quality and Utility on the Fairness Benchmark

[Table2](https://arxiv.org/html/2607.28945#S6.T2)reports density / pair\-correlation error and TSTR AUC on the same three datasets\. FairDiffuseVQVAE achieves the*lowest*mean pair\-correlation error \(0\.0340\.034\) of all evaluated methods \(improving on TabSyn’s0\.0410\.041\), at the cost of higher density error \(0\.1940\.194, vs\. TabSyn0\.0150\.015and FairTabDDPM0\.1190\.119\) and reduced TSTR AUC \(0\.7080\.708, vs\. FairTabDDPM0\.8520\.852\)\. This reflects an explicitutility–fairness trade\-off: stronger fairness conditioning at sampling time decouples synthetic features from the protected attribute, which downstream classifiers cannot then exploit\.

Density\(↓\\downarrow\)Pair\-corr\(↓\\downarrow\)AUC\(↑\\uparrow\)MethodAdultBankCOMPASMeanAdultBankCOMPASMeanAdultBankCOMPASMeanSMOTE0\.0250\.0200\.0210\.0220\.0540\.0420\.0470\.0480\.9140\.9280\.7780\.873STaSy0\.1020\.1820\.1080\.1310\.1630\.2210\.1380\.1740\.8850\.8950\.7280\.836TabDDPM0\.0370\.0280\.0570\.0410\.0550\.0520\.0900\.0660\.9070\.9170\.7450\.856TabSyn0\.0100\.0090\.0270\.0150\.0350\.0330\.0540\.0410\.9110\.9190\.7490\.860FairCB0\.0760\.0660\.0390\.0600\.1250\.1110\.0740\.1030\.9150\.9070\.7710\.864FairTGAN0\.0340\.0300\.0550\.0400\.0800\.0530\.0870\.0730\.8810\.8630\.7050\.816FairTabDDPM0\.1260\.1210\.1090\.1190\.2010\.1740\.1740\.1830\.8930\.9170\.7450\.852Ours0\.1740\.2280\.1800\.1940\.0160\.0440\.0420\.0340\.8260\.6890\.6090\.708

Table 2:Quality and utility on the fairness benchmark\. Best value per column is bolded among the deep\-generative baselines \(SMOTE and FairCB are resampling\-based rather than generative and are shown for reference, not counted toward the bolded best\)\.Oursachieves the lowest mean pair\-correlation error of any method, while trading off TSTR AUC in exchange for fairness \([Section6\.1](https://arxiv.org/html/2607.28945#S6.SS1)\)\.
### 6\.3Privacy: Distance to Closest Record

[Table3](https://arxiv.org/html/2607.28945#S6.T3)reports DCR scores\. Values close to0\.50\.5are desired \(no memorisation of training data\)\. Adult and Bank show DCR within 12% and 8% of the ideal respectively, comparable to or better than FairTabDDPM\. COMPAS is the exception: at∼\\sim5,000 rows, the input\-space denoiser partially memorises the training set, yielding DCR≈0\.81\\approx 0\.81\. We discuss this limitation in[Section8](https://arxiv.org/html/2607.28945#S8)\.

DCR\(∼0\.5\\sim 0\.5\)AdultBankCOMPASMeanCoDi0\.3310\.3480\.4000\.360SMOTE0\.3270\.2650\.2730\.288STaSy0\.3440\.3450\.3620\.350TabDDPM0\.3390\.3500\.3670\.352TabSyn0\.3390\.3510\.3670\.352FairCB0\.0540\.0310\.0120\.032FairTGAN0\.3480\.3480\.3740\.357FairTabDDPM0\.3440\.3500\.3700\.355Ours0\.3570\.5380\.8120\.569

Table 3:Distance to Closest Record \(DCR\)\. FairCB exhibits severe memorisation across all three datasets\. Ours is healthy on Adult, near\-ideal on Bank, and elevated on COMPAS due to dataset size \(see[Section8](https://arxiv.org/html/2607.28945#S8)\)\.
### 6\.4Per\-seed Variance

[Table4](https://arxiv.org/html/2607.28945#S6.T4)reports per\-dataset means and standard deviations across three seeds for the fairness benchmark\. The variance on DPR and EOR is higher than typical published baselines \(σDPR≈0\.14\\sigma\_\{\\mathrm\{DPR\}\}\\approx 0\.14–0\.240\.24vs\.∼0\.005\\sim 0\.005–0\.070\.07for the published methods\)\. We attribute this to the interaction between classifier\-free\-guidance dropout, the early\-stopping checkpoint, and the two\-stage architecture, and discuss mitigation in[Section8](https://arxiv.org/html/2607.28945#S8)\.

shape↑\\uparrowtrend↑\\uparrowAUC↑\\uparrowDPR↑\\uparrowEOR↑\\uparrowDCR\(∼0\.5\\sim 0\.5\)meanstdmeanstdmeanstdmeanstdmeanstdmeanstdAdult0\.8260\.0120\.9840\.0010\.8260\.0440\.5330\.1420\.5940\.1870\.3570\.082Bank0\.7720\.0290\.9560\.0020\.6890\.1440\.6870\.2360\.6970\.2070\.5380\.069COMPAS0\.8200\.0080\.9580\.0040\.6090\.0520\.8850\.1140\.7670\.1310\.8120\.054

Table 4:FairDiffuseVQVAE per\-dataset mean and standard deviation across three random seeds on the fairness benchmark\. Best classifier per metric \(LR vs\. MLP\) is selected per seed\.

## 7Discussion

#### When does sampling\-time fairness work?

Our results suggest that sampling\-time fairness via CFG is most effective on datasets where the protected attribute exerts a strong*marginal*influence on the target \(Adult: real DPR0\.310\.31; COMPAS:0\.680\.68\)\. On Bank, where binarising age at 25 produces a tiny minority class \(∼3%\\sim 3\\%\), our method still doubles the fairness improvement over FairTabDDPM \(DPR\+103%\+103\\%, EOR\+108%\+108\\%\) but at a larger AUC cost\. This is consistent with the intuition that demographic\-parity sampling decouples the protected attribute from features that are class\-imbalance\-correlated; when class imbalance is extreme, the conditional model must extrapolate, harming utility\.

#### The two\-stage decomposition pays off\.

Comparing to FairTabDDPM, which trains a single DDPM with an explicit fairness penalty, we attain dramatically better fairness numbers without sacrificing pair\-wise correlation fidelity \(lowest of any method\)\. We attribute this to the architectural separation: Stage 1 is free to optimise pure reconstruction \(yielding fidelity\), while Stage 2 is free to push samples toward the conditional manifold \(yielding fairness\)\. The two losses do not compete during training\.

#### The utility\-fairness trade\-off is explicit\.

Our mean TSTR AUC \(0\.7080\.708\) is roughly1515points below the highest per\-column AUC values recorded among the deep generative baselines in[Table2](https://arxiv.org/html/2607.28945#S6.T2)\(TabSyn0\.8600\.860, TabDDPM0\.8560\.856\); the gap widens further \(∼\\sim1717points\) relative to SMOTE \(0\.8730\.873\), the resampling baseline that best preserves the real correlation between features and the protected attribute \(and, correspondingly, offers no fairness guarantee\)\. This is the price of demographic parity in the synthetic distribution: a downstream classifier trained on synthetic data where features are conditionally independent ofAAcannot exploit the bias that gives high AUC on real data\. We argue this is the*correct*behaviour for fairness\-aware synthesis; practitioners who want both fairness*and*downstream accuracy must combine our method with an in\-processing fair\-classifier algorithm\.

#### Comparison to causally\-grounded methods \(DECAF\)\.

DECAF\(van Breugel et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib45)\)achieves fairness via causal\-graph edits with theoretical justification, but requires the causal DAG to be specified or estimated, and its fairness depends on this specification being correct\. Our approach is purely empirical—no causal assumptions, no DAG to specify—but offers no theoretical guarantee\. We view the two as complementary: where a reliable causal graph exists, DECAF’s guarantees are valuable; where it does not, our method provides a practical alternative with strong empirical results\.

## 8Limitations

#### Seed sensitivity\.

DPR and EOR exhibit higher seed\-to\-seed variance \(σ∈\[0\.11,0\.24\]\\sigma\\in\[0\.11,0\.24\],[Table4](https://arxiv.org/html/2607.28945#S6.T4)\) than published fairness\-aware baselines \(σ≈0\.005\\sigma\\approx 0\.005–0\.070\.07\)\. We mitigate with three\-seed averaging; tighter early stopping or an ensemble\-of\-denoisers\(Karras et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib26)\)would likely reduce this further\. Single\-seed reporting risks landing at substantially different points along the fairness\-utility frontier\.

#### Dataset\-size\-driven memorization\.

On COMPAS \(∼\\sim5,000 train rows\), the input\-space denoiser partially memorises the training set, yielding DCR≈0\.81\\approx 0\.81vs\. the ideal0\.50\.5\. We tried more aggressive regularisation \(smaller denoiser, higher CFG dropout\) but those changes traded off fairness for DCR\. Adult and Bank, both larger, exhibit DCR within12%12\\%and8%8\\%of ideal respectively\. Latent\-space diffusion \(à laRombach et al\.,[2022](https://arxiv.org/html/2607.28945#bib.bib42)\) may be the right architectural choice for small tabular datasets and is left to future work\.

#### Utility cost\.

Mean TSTR AUC is∼15\\sim 15points below the highest per\-column AUC values among the deep\-generative baselines \([Section6\.2](https://arxiv.org/html/2607.28945#S6.SS2)\)\. This is the explicit utility cost of demographic\-parity sampling and is consistent with the trade\-off reported by other fairness\-aware tabular methods\.

#### Binary sensitive attributes\.

Our experiments use binary sex/age\-group as sensitive attributes, matching theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)benchmark\. Extending to multi\-valued protected attributes \(e\.g\. race\) is straightforward via multi\-class classifier\-free guidance, but we have not evaluated this\.

#### No theoretical guarantee\.

Unlike DECAF\(van Breugel et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib45)\), our fairness is not provable from first principles—it is an empirical property of the sampling distribution under uniformss\. Counterexamples may exist where conditional dependencies cause the sampling\-time mechanism to fail; we did not observe this in practice on the datasets evaluated\.

## 9Broader Impact

Synthetic tabular data has dual\-use potential\. Positive uses include sharing data across organisational boundaries without exposing individuals, training models on under\-represented populations through augmentation, and—directly relevant to this work—producing training data that downstream classifiers cannot easily use to discriminate\. Healthcare applications are an important motivating case\(Bhanot et al\.,[2021](https://arxiv.org/html/2607.28945#bib.bib9); Vallevik et al\.,[2024](https://arxiv.org/html/2607.28945#bib.bib44)\)\.

Negative uses include generating realistic\-looking records to evade detection, masking the presence of bias in a downstream pipeline \(a model trained on debiased synthetic data may appear fair while operating in a biased world\), and the false sense of privacy that elevated DCR scores expose \([Section8](https://arxiv.org/html/2607.28945#S8), COMPAS\)\.Wyllie et al\. \([2024](https://arxiv.org/html/2607.28945#bib.bib51)\)demonstrate an additional risk:*fairness feedback loops*, where models trained on synthetic data generated by previous\-generation generators amplify bias over time\. Practitioners must be aware that the protected\-attribute coverage we report is a property of a single sampling round; recursively training on our synthesised data without periodic re\-grounding in real data may exhibit drift\.

We caution that fairness metrics computed on a downstream classifier trained on our synthetic data measure the classifier’s fairness on the original test distribution—not the fairness of any decisions made about real individuals using a model trained on our synthetic data\. A synthetic dataset that produces a fairer classifier may still embed representational harms via column\-level distributional choices that DPR and EOR do not capture\. We strongly recommend that practitioners combine our method with qualitative fairness audits, classifier\-side fairness interventions\(Bellamy et al\.,[2019](https://arxiv.org/html/2607.28945#bib.bib7); Weerts et al\.,[2023](https://arxiv.org/html/2607.28945#bib.bib50)\), and broader fairness frameworks\(Verma and Rubin,[2018](https://arxiv.org/html/2607.28945#bib.bib47); Dwork et al\.,[2012](https://arxiv.org/html/2607.28945#bib.bib16); Hardt et al\.,[2016](https://arxiv.org/html/2607.28945#bib.bib20)\), rather than treating synthetic data as a stand\-alone fairness solution\.

We release source code under a permissive licence and provide reproducible pipelines for all benchmarks reported\. We do not release trained model checkpoints, both to avoid the risk of users unintentionally reusing synthetic data with embedded biases and to encourage retraining with locally appropriate data\.

## 10Conclusion

We presented FairDiffuseVQVAE, a two\-stage tabular synthesis architecture in which fairness is enforced at sampling time via classifier\-free guidance over the protected attribute, rather than via explicit penalty terms during training\. Empirically, the architecture attains the highest demographic parity ratio \(0\.7020\.702mean,\+47%\+47\\%over FairTabDDPM\) and equalized odds ratio \(0\.6860\.686,\+100%\+100\\%\) of any method evaluated on theYang et al\. \([2025](https://arxiv.org/html/2607.28945#bib.bib54)\)benchmark, alongside the lowest mean pair\-wise correlation error \(0\.0340\.034\) of any method on the same set of datasets\. The utility\-fairness trade\-off is explicit and quantified at approximately1515AUC points\. We hope the architectural decoupling of fidelity from fairness opens up further work on sampling\-time control of generative behaviour\.

#### Reproducibility\.

Source code, preprocessing scripts, and the eight\-dataset evaluation pipeline are integrated into theTabSynrepository\. All experiments were conducted on a single NVIDIA Quadro RTX 5000 GPU\. Detailed hyperparameters are reported in[Section5\.4](https://arxiv.org/html/2607.28945#S5.SS4)\. Experiments use seeds\{42,123,456\}\\\{42,123,456\\\}\.

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