树木与流形互转：决策树与扩散模型的统一框架

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

May 1, 2026

作者: Sai Niranjan Ramachandran, Suvrit Sra

cs.AI

摘要

决策树与扩散模型表面上是截然不同的模型类别——前者离散分层，后者连续动态。本研究通过建立分层决策树与特定极限状态下扩散过程之间精确的数学对应关系，实现了二者的统一。我们的统一框架揭示了一个共享的优化原理：全局轨迹评分匹配（GTSM），其中梯度提升（在理想化版本中）具有渐近最优性。我们通过两个关键实践案例凸显研究的理论价值：\treeflow 在表格数据生成任务中实现媲美主流方法的生成质量，同时具备更高保真度和2倍计算加速；\dsmtree 作为一种新型蒸馏方法，将分层决策逻辑迁移至神经网络，在多个基准测试中与教师模型性能差距控制在2%以内。

English

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: 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.