Constrained Tabular Generation: Exact Conditioning of Arbitrary Markov Processes

Tabular data generation supports privacy-preserving data sharing, minority-class augmentation, test-database generation, and missing-value imputation. These often require generated rows to satisfy constraints on arbitrary subsets of columns with probability one, while matching the distribution of real rows satisfying them. We study this as *constrained tabular generation*. Existing methods are limited to pinned values, sacrifice distributional fidelity for constraint satisfaction, or restrict exact conditioning to continuous diffusions. Using generator matching, we unify tabular flow, diffusion, and jump models through Markov generators and introduce $\mathrm{T}\mathrm{AB}\mathrm{J}\mathrm{UMP}$, a pure-jump model for both numerical and categorical columns. We apply Doob's $h$-transform to general Markov generators, deriving exact conditioning through additive drift corrections for diffusions and multiplicative reweighting of jump rates, both learnable with a consistent objective. This characterizes which processes admit corrections: deterministic flows do not, since the transform leaves the generator unchanged, although in special cases flows admit training-free but biased conditioning using a mean-field approximation of their endpoint posterior. We amortize conditioning through a trainable guide that takes constraints as input, keeps the unconditional generator frozen, and generalizes to unseen constraints across arities, modalities, types, and selectivities. Across eight datasets, our methods improve unconditional fidelity and outperform imputation-, penalty-, and LLM-based baselines in both constraint satisfaction and conditional fidelity.