Conditioning Tree-Based Diffusions and Flows for Probabilistic Tabular Regression

Abstract:Tree-based diffusion models fit flexible conditional predictive distributions for tabular regression without a neural density estimator, but they inherit their design defaults---noising path, parameterization, training distribution, features, sampler---from the neural setting. We show these defaults are the binding constraint: what a gradient-boosted ensemble actually solves is a supervised regression problem whose conditioning they determine. We present DiffGBM, which makes them explicit along two axes. First, a Gaussian-path flow-matching trainer for $p(y \mid x)$ that learns a velocity field directly and recovers the score algebraically, admitting few-step deterministic ODE sampling. Second, we expose the score-side recipe---residualization, EDM-style preconditioning, log-sigma time sampling, noise-level features, loss weighting, and histogram resolution---as jointly tunable axes over a shared LightGBM surface rather than one frozen bundle. This \emph{score-flex} space represents the published recipe as a special case; across eleven tabular benchmarks under fold-0 tuning, folds-1--5 evaluation, and a matched 40-trial budget and sampler, the selected configurations beat that baseline on \emph{every} dataset (paired Wilcoxon $11/0$, $p<10^{-3}$), with the best aggregate CRPS skill (0.725 vs.\ 0.699) of any row. The two rows are complementary: score-flex buys accuracy with a stochastic sampler and is the slowest row, while flow matching is the cheapest sampler ($5.2\times$ faster than the published baseline) and the best-calibrated DiffGBM row. Tuned non-diffusion baselines still win individual datasets, and stochastic ($\varepsilon>0$) flow samplers do not Pareto-dominate the deterministic corner.

25 pages, 2 figures. Code: this http URL

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2607.28864 [stat.ML]

(or arXiv:2607.28864v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.28864 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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