[2605.00414] Trees to Flows and Back: Unifying Decision Trees and Diffusion Models

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Computer Science > Machine Learning

arXiv:2605.00414 (cs)

[Submitted on 1 May 2026 (v1), last revised 21 May 2026 (this version, v2)]

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

Authors:Sai Niranjan Ramachandran, Suvrit Sra<br>View a PDF of the paper titled Trees to Flows and Back: Unifying Decision Trees and Diffusion Models, by Sai Niranjan Ramachandran and 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.

Comments:<br>12 pages (main), 68 pages (inclusive of appendix), Accepted in the Forty-Third International Conference on Machine Learning (ICML) 2026

Subjects:

Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI)

Cite as:<br>arXiv:2605.00414 [cs.LG]

(or<br>arXiv:2605.00414v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.00414

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arXiv-issued DOI via DataCite

Submission history<br>From: Sai Niranjan Ramachandran [view email]<br>[v1]<br>Fri, 1 May 2026 05:19:54 UTC (8,277 KB)

[v2]<br>Thu, 21 May 2026 04:49:57 UTC (8,277 KB)

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