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

rsn243

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.

semessier

this lacks the math for any bold claims

niksmather

Apologies if I didn't understand the paper, but why do you want to apply diffusion models to tabular datasets in the first place? Do we think they'll be better than decision trees? Is there some tabular problem that can be handled by diffusion but not trees?

gorold

Figure 1 definitely cleared up any misunderstandings I had about the paper

henrydark

Is the code available somewhere?