将决策树与扩散模型统一为同一优化框架，提升生成效率与逻辑可解释性。
Trees to Flows and Back: Unifying Decision Trees and Diffusion Models
- 通过极限情形建立决策树与扩散过程的数学对应关系。
- 提出全局轨迹得分匹配原则，梯度提升在理想下最优。
- 实现更高效生成与决策逻辑迁移，性能接近教师模型。
决策树与扩散模型看似属于不同范式：前者离散且分层，后者连续且动态。本文通过在适当极限条件下建立两者的清晰数学对应关系，实现了二者的统一。该统一揭示了共享的优化原则——全局轨迹得分匹配（GTSM），在理想化版本中梯度提升为此目标的渐近最优解。通过两个关键应用验证其价值： reeflow 在表格数据生成上达到竞争性质量，精度更高且计算速度提升2倍； smtree 是一种新型知识蒸馏方法，将层次化决策逻辑迁移到神经网络，在多个基准测试中仅落后教师模型2%以内。
原文摘要 · Abstract (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: \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.
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