{"paper":{"title":"Trees to Flows and Back: Unifying Decision Trees and Diffusion Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Decision trees correspond to diffusion processes in limiting regimes and share the Global Trajectory Score Matching optimization principle.","cross_cats":["cond-mat.stat-mech","cs.AI"],"primary_cat":"cs.LG","authors_text":"Sai Niranjan Ramachandran, Suvrit Sra","submitted_at":"2026-05-01T05:19:54Z","abstract_excerpt":"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, wh"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes in appropriate limiting regimes. 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