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Exponential Family Variational Flow Matching for Tabular Data Generation
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Proposes EF-VFM, an exponential-family extension of variational flow matching with moment (sufficient-statistic) matching and a Bregman-divergence view, instantiated as TabbyFlow for mixed-type tabular data generation.
Problem
Generating tabular data with mixed continuous and discrete columns via flow matching, where existing flow/diffusion methods handle heterogeneous feature types awkwardly.
Approach
Use exponential-family variational distributions per column inside Variational Flow Matching so that training reduces to matching sufficient statistics (MSE for continuous, cross-entropy for categorical), and show VFM equals minimizing a Bregman divergence induced by the conjugate dual of the log-normalizer.
Key results
- TabbyFlow achieves the best average alpha-precision (98.69) and ranks first on that metric, versus 98.67 for TabSyn.
- TabbyFlow reports the lowest average Wasserstein distance (train 1.7, test 2.1) among compared methods.
- On machine learning efficiency, TabbyFlow averages 0.854 versus 0.858 for TabSyn, so it is slightly below TabSyn on downstream utility.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TabbyFlow's exponential-family variational flow matching instead of TabDiff | Tabular data generation · Shape average | error rate (%): 1.17 -> 1.08 | Helped |
| Use TabbyFlow's exponential-family variational flow matching instead of TabDiff | Tabular data generation · Trend average | error rate (%): 1.80 -> 1.77 | Helped |
| Use TabbyFlow instead of TabSyn | Tabular data generation · α-Precision average | α-Precision: 98.67 -> 98.69 | Helped |
| Use TabbyFlow instead of TabDiff | Tabular data generation · β-Recall average | β-Recall: 50.37 -> 49.35 | Hurt |
| Use TabbyFlow instead of TabSyn | Tabular data generation · Wasserstein distance (Train) | Wasserstein distance: 2.2 ± 0.4 -> 1.7 ± 0.7 | Helped |
| Use TabbyFlow instead of TabSyn | Tabular data generation · Wasserstein distance (Test) | Wasserstein distance: 3.0±0.3 -> 2.1±0.4 | Helped |
| Use TabbyFlow instead of TabSyn | Synthetic-data downstream tasks · MLE average | MLE: .858 -> .854 | Hurt |
Surprising findings
- TabbyFlow is slightly below TabSyn on machine learning efficiency despite leading on several fidelity metrics, which the authors attribute to MLE not fully capturing quality.
- TabbyFlow does not beat the best baseline on beta-recall average (49.35 vs 50.37 for TabDiff).
Limitations
- Only Gaussian and categorical (and Bernoulli) exponential families were used; other families were not explored.
- Relies on linear-in-x1 conditional velocity fields so that only the mean needs matching; the full sufficient statistics are not matched.
- Natural gradient descent / information geometry aspects are discussed but not studied empirically.
Experimental setup
Datasets: Adult Default Shoppers Magic Beijing News
Benchmarks: Adult Default Shoppers Magic Beijing News
Metrics: Wasserstein distance Shape Trend alpha-precision beta-recall C2ST DCR machine learning efficiency (AUC/RMSE)
Baselines: CTGAN TVAE GOGGLE TabDDPM TabSyn TabDiff
Builds on: Variational Flow Matching Conditional Flow Matching TabSyn TabDiff
Closest papers by meaning
- TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation (ICLR 2025 · similarity 0.88)
- Variational Flow Matching for Graph Generation (NeurIPS 2024 · similarity 0.88)
- Continuous Diffusion for Mixed-Type Tabular Data (ICLR 2025 · similarity 0.88)
- Discrete Flow Matching (NeurIPS 2024 · similarity 0.86)
- CTSyn: A Foundation Model for Cross Tabular Data Generation (ICLR 2025 · similarity 0.86)
- TabNAT: A Continuous-Discrete Joint Generative Framework for Tabular Data (ICML 2025 · similarity 0.86)
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