[Submitted on 1 May 2026 (
[v1](https://arxiv.org/abs/2605.00414v1)), last revised 21 May 2026 (this version, v2)]# Title:Trees to Flows and Back: Unifying Decision Trees and Diffusion Models
[View PDF](/pdf/2605.00414)
Abstract:Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes in appropriate limiting regimes. Our unification reveals a shared optimization principle: \emph{Global Trajectory Score Matching (GTSM)}, for which gradient boosting (in an idealized version) is asymptotically optimal. We underscore the conceptual value of our work through two key practical instantiations: \treeflow, which achieves competitive generation quality on tabular data with higher fidelity and a 2\times computational speedup, and \dsmtree, a novel distillation method that transfers hierarchical decision logic into neural networks, matching teacher performance within 2% on many benchmarks.
Submission history #
From: Sai Niranjan Ramachandran [[view email](/show-email/4bd0d387/2605.00414)]
**Fri, 1 May 2026 05:19:54 UTC (8,277 KB)**
[[v1]](/abs/2605.00414v1)**[v2]** Thu, 21 May 2026 04:49:57 UTC (8,277 KB)
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