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

arXiv: https://arxiv.org/abs/2605.00414 · HTML: https://mlsanity.com/paper/2605.00414/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 6 of its 57 references that are in the map.
- First posted on arXiv 1 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 6 of 6)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [Do Diffusion Models Learn Semantically Meaningful and Efficient Representations?](https://mlsanity.com/paper/2402.03305/) (2024)

## Abstract (arXiv)

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× computational speedup, and dsmtree, a novel distillation method that transfers hierarchical decision logic into neural networks, matching teacher performance within 2% on many benchmarks.