Geometry-Aware Tabular Diffusion

Tabular data plays an important role in many fields and industries, including those with elevated privacy considerations and risks. As such, there is a rising interest in generating high-quality synthetic proxies for real tabular data as a means of reducing privacy risk and proprietary data exposure. With tabular diffusion models (TDMs) demonstrating leading performance in synthesizing such data, understanding and measuring the privacy risks associated with these models is imperative. Leveraging state-of-the-art membership inference attacks for TDMs in both black- and white-box settings, this work quantifies the impact of training setup, synthesis choices, and attacker knowledge on privacy leakage. Moreover, the results demonstrate that adversaries need not have perfect knowledge of the training setup, identical data distributions, or massive compute resources to construct successful attacks. Finally, the pitfalls associated with applying heuristic privacy metrics, such as distance-to-closest record, are revealed.

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 introduce FairDiffuseVQVAE, a two-stage architecture that decouples fidelity from fairness: a vector-quantized autoencoder with a row-level discriminator (Stage1, 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 (Stage2). 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 the Adult, Bank and COMPAS datasets, FairDiffuseVQVAE achieves the highest mean Demographic Parity Ratio ($0.702$, $+47\%$ over FairTabDDPM) and Equalized Odds Ratio ($0.686$, $+100\%$). It also attains the lowest mean pair-wise correlation error ($0.034$) of any published method, while explicitly trading \sim$$15 AUC points for these fairness gains.

Diffusion-based generators set the current state of the art for synthetic tabular data. These methods approach but rarely exceed real-data utility, and closing this synthetic-real gap has so far been pursued exclusively at training time, via architectural advances, scaling, and retraining of monolithic generators. The inference-time alternative, i.e., refining the outputs of a pre-trained backbone with parameters left untouched, has remained largely unexplored for tabular synthesis. We introduce TARDIS (Tabular generation through Refinement, Distillation, and Inference-time Sampling), an inference-time refinement framework that operates on a frozen pre-trained backbone, configured per dataset by a Tree-structured Parzen Estimator search over score-level guidance during reverse diffusion, with each trial's objective set by an inner grid search over post-hoc sample selectors and an optional soft-label distillation step. The search space encodes a single mathematical pattern we name Bidirectional Chamfer Refinement (BCR): the symmetric Chamfer functional between synthetic and real samples is minimized both continuously, via a score-level gradient, and discretely, via batch-ranking post-generation. The per-dataset search recovers BCR-aligned configurations on most datasets, evidence for BCR as the dominant refinement pattern. Across 15 binary, multiclass, and regression benchmarks TARDIS achieves a median +8.6% downstream-task improvement over models trained on real data (95% CI [+3.3, +16.4], Wilcoxon p=0.016, 11/15 strict wins) and improves over the TabDiff backbone on all 15 datasets (mean +12.9%, p<10^-4), matching the backbone on manifold fidelity, diversity, and sample-level privacy. Inference-time refinement of a pre-trained tabular diffusion backbone reaches and exceeds real-data utility in 1 to 80 minutes on a single consumer-grade GPU.