Trees to Flows and Back: Unifying Decision Trees and Diffusion Models
For researchers in generative modeling and decision tree learning, this unification provides a new theoretical foundation and practical algorithms that improve efficiency and performance.
This work establishes a mathematical correspondence between decision trees and diffusion models, revealing a shared optimization principle (GTSM). The resulting methods achieve competitive generation quality on tabular data with 2× speedup and a distillation method that matches teacher performance within 2% on benchmarks.
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.