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

2026-06-08

AI Summary

This work addresses the challenges of generating high-dimensional, low-sample-size (HDLSS) tabular data, where issues such as ill-posed density estimation, strong local correlations, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness hinder realistic synthesis. To overcome these difficulties, the authors propose a block–subunit generative framework that partitions high-dimensional features into a small number of latent blocks. Global dependencies are modeled through shared low-dimensional subunit latent variables, and—uniquely—the approach integrates diffusion priors with a copula-based decoder to enable stable dependency learning in the low-dimensional block latent space. Coupled with flexible marginal distribution modeling and an explicit mechanism for handling missing data, the method significantly enhances the fidelity and stability of synthetic data, outperforming existing unstructured tabular generation approaches.

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.

Problem

• High-Dimensional Low-Sample Size
• Tabular Data Generation
• Ill-conditioned Density Learning
• Structured Missingness
• Non-Gaussian Marginals

Innovation

• block-subunit diffusion
• high-dimensional tabular generation
• copula-based dependence
• structured missingness
• low-sample-size generative modeling