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

TL;DR

This paper unifies decision trees and diffusion models through a mathematical correspondence, revealing shared optimization principles and enabling practical methods like reeflow and extsc{DSTM} for improved data generation and model distillation.

Contribution

It establishes a formal link between hierarchical decision trees and diffusion processes, introducing the GTSM principle and practical algorithms that outperform existing methods.

Findings

reeflow achieves higher fidelity and 2× faster generation on tabular data.

extsc{DSTM} effectively distills decision logic into neural networks, matching teacher performance within 2%.

The unification offers new insights into model optimization and practical applications.

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.