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

Sai Niranjan Ramachandran; Suvrit Sra

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arXiv · 2605.00414

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

Sai Niranjan Ramachandran·Suvrit Sra

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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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Sai Niranjan Ramachandran, Suvrit Sra. 2026-05-01. Trees to Flows and Back: Unifying Decision Trees and Diffusion Models. https://arxiv.org/abs/2605.00414

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