Trees to Flows and Back: Unifying Decision Trees and Diffusion Models

• URL: http://arxiv.org/abs/2605.00414v1
• Date: Fri, 01 May 2026 05:19:54 GMT
• Title: Trees to Flows and Back: Unifying Decision Trees and Diffusion Models
• Abstract summary: This work unifies the two by establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes.<n>Our unification reveals a shared optimization principle: emphGlobal Trajectory Matching Score (GTSM)<n>We underscore the conceptual value of our work through two key practical instantiations: treeflow and dsmtree.
• Score: 20.34299008085434
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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