BSTabDiff: Block-Subunit Diffusion Priors for High-Dimensional Tabular Data Generation

Al Zadid Sultan Bin Habib, Md Younus Ahamed, Prashnna Kumar Gyawali, Gianfranco Doretto, Donald Adjeroh

Keywords: Block-structured generative modeling, High-dimensional low-sample size (HDLSS), Synthetic tabular data, Tabular diffusion models

TL;DR: We propose BSTabDiff, a block-subunit HDLSS tabular generator that learns dependence in a compact block-latent space ($M\ll m$) with diffusion/flow priors and copula decoding, enabling stable synthesis when $n\ll m$.

Abstract: High-Dimensional Low-Sample Size (HDLSS) tabular domains (e.g., omics) are characterized by $n \ll m$, where $n$ = number of samples, and $m$ = number of features. Such domains often exhibit strong local correlation groups, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness, making direct density learning in $\mathbb{R}^m$ ill-conditioned since $n \ll m$. We propose BSTabDiff, a block-subunit generative framework that partitions the $m$ observed features into $M$ latent blocks ($M \ll m$) and generates each block via a shared low-dimensional subunit variable, concentrating global dependence learning in the compact block-latent space $\mathbb{R}^M$ while decoding to the full feature space with copula-driven dependence, flexible per-feature marginals, and explicit missingness mechanisms. BSTabDiff supports modern deep priors on block latents, including diffusion and normalizing flows, enabling stable synthesis and controllable benchmark generation in the HDLSS regime. Empirically, BSTabDiff produces more realistic and stable high-dimensional synthetic data when compared with unstructured tabular generators on HDLSS data.

Submission Number: 152