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.

Many organizations want to share or reuse tabular data, such as spreadsheets, without exposing sensitive records. This is hard because good synthetic data must preserve relationships between columns: for example, how age, income, education, and hours worked tend to move together. Many existing methods ask a large neural network to discover these relationships on its own. We instead give the model a simple description of each pair of columns: an angle for direction and a length for distance, both computed from the data values. The model is also trained to predict these relationships while learning to generate synthetic rows. Across ten benchmark datasets, this makes synthetic data look more like real data, improving how well individual columns match by 27% and how well column relationships match by 20% compared with TabDiff, a strong recent baseline. The method also uses 3.5 times fewer parameters on average and trains 1.7 times faster. The same idea also works in other model designs, suggesting it is a reusable signal rather than a one-off architecture trick. This work can make synthetic data tools more practical, though synthetic data alone does not guarantee privacy.