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

A formal correspondence between hierarchical decision trees and diffusion processes yields a shared optimization objective called Global Trajectory Score Matching, where idealized gradient boosting is asymptotically optimal. Two practical results follow: TreeFlow matches diffusion model generation quality on tabular data with 2x speedup, and DSMTree distills decision tree logic into neural networks within 2% of teacher performance on multiple benchmarks. Accepted at ICML 2026.