Geometry-Aware Tabular Diffusion

Tabular synthesis is critical for privacy-preserving sharing and augmentation, yet diffusion models rely on implicit mechanisms to capture inter-column relationships. We introduce Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. Our MLP instantiation achieves state-of-the-art benchmark performance while using $3.5\times$ fewer parameters on average (up to $25\times$ for classification tasks): on ten datasets, it wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility (F1/RMSE), reducing Shape and Trend error by 27% and 20%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset cells. A matched ablation shows supervision (not extra inputs or capacity) drives the gain. This shows explicit relational supervision is a portable inductive bias for tabular diffusion.