Generating mixed-type tabular data requires jointly modeling diverse feature distributions and their complex cross-column dependencies. Variational flow matching handles distinct endpoints via factorized distributions, yet leaves feature-specific processing and cross-column interactions implicit within a shared backbone. We introduce Feature-wise Unified Specialization with cross-column Exchange (FUSE) to explicitly separate these roles. FUSE applies separate adaptive mixture modules to numerical and categorical features, allowing each feature to combine shared specialized subnetworks, while joint attention preserves information exchange across all columns. We also characterize the excess population risk from restricted conditioning contexts and bound the continuous Wasserstein generation error by endpoint-prediction risk. Comprehensive experiments on eight tabular datasets demonstrate that FUSE achieves strong and consistent performance across distributional fidelity and downstream utility metrics.
Mixed continuous--categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.
Tabular data generation considers a large table with multiple columns -- each column comprised of numerical, categorical, or sometimes ordinal values. The goal is to produce new rows for the table that replicate the distribution of rows from the original data -- without just copying those initial rows. The last 4 years have seen enormous progress on this problem, mostly using computational expensive methods that employ one-hot encoding, VAEs, and diffusion. This paper describes a new approach to the problem of tabular data generation. By employing copula transformations and modeling the distribution as a kernel density estimate we can nearly match the accuracy and leakage-avoidance achievements of the previous methods, but with almost no training time. Our method is very scalable, and can be run on data sets orders of magnitude larger than prior state-of-the-art on a simple laptop. Moreover, because we employ kernel density estimates, we can store the model as a coreset of the original data -- we believe the first for generative modeling -- and as a result, require significantly less space as well. Our code is available here: \url{https://github.com/tabkde/tabkde-main}
Synthetic tabular data are valued for preserving not just column-wise marginals but inter-column dependency, which carries much of the minority-class signal in domains such as fraud detection and clinical risk. Yet standard certification is largely blind to it: a fully-factorized baseline that destroys all inter-column dependency still appears nearly real under the commonly reported linear classifier two-sample test (C2ST), and is only mildly penalized by pairwise Trend scores. This is a known weakness of linear detection scores, which we confirm on four benchmarks. We therefore decompose a stronger, gradient-boosted C2ST score into marginal, dependency, and numerical-categorical cross terms, each read against a zero-dependency reference and a real-data oracle. Applied to representative flow-matching (TabbyFlow/EF-VFM) and diffusion (TabDiff) generators, it finds a persistent dependency gap of comparable magnitude in both, tracking what their objectives share rather than anything specific to one. Dependency is necessary for minority-class utility, since a zero-dependency reference collapses it, yet the generators' residual gaps coincide with much smaller shortfalls that do not track the measured gap. The gap is neither a structural limitation of mean-field objectives nor closed by a 16x capacity increase where training is clean, which motivates supervising dependency directly in the objective as the next intervention to test.