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

2026-05-01

AI Summary

This work bridges the fundamental gap between decision trees and diffusion models, which respectively operate in discrete hierarchical structures and continuous dynamic processes. Through asymptotic analysis, it establishes—for the first time—a rigorous mathematical correspondence between the two under specific conditions, yielding a unified framework grounded in a shared optimization principle termed Global Trajectory Score Matching (GTSM). Leveraging this insight, the authors develop two practical bidirectional models: TreeFlow, which achieves higher fidelity and a 2× speedup in tabular data generation, and DSTree, a distillation approach that attains over 98% of the teacher model’s performance across multiple benchmarks.

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.

Problem

• decision trees
• diffusion models
• unification
• hierarchical models
• continuous dynamics

Innovation

• Global Trajectory Score Matching
• decision trees
• diffusion models
• TreeFlow
• DSTree