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

Researchers have established a mathematical correspondence between hierarchical decision trees and diffusion processes, unifying the two model classes under a shared optimization principle called Global Trajectory Score Matching. The work yields two practical applications: TreeFlow, which achieves competitive tabular data generation with higher fidelity and 2× speedup, and DSMTree, a distillation method that transfers decision logic into neural networks within 2% of teacher performance. The unification reveals gradient boosting as asymptotically optimal for the shared framework, bridging discrete and continuous machine learning approaches.

Computer Science Machine Learning Submitted on 1 May 2026 v1 https://arxiv.org/abs/2605.00414v1 , last revised 21 May 2026 this version, v2 Title:Trees to Flows and Back: Unifying Decision Trees and Diffusion Models View PDF /pdf/2605.00414 Abstract: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. Submission history From: Sai Niranjan Ramachandran view email /show-email/4bd0d387/2605.00414 Fri, 1 May 2026 05:19:54 UTC 8,277 KB v1 /abs/2605.00414v1 v2 Thu, 21 May 2026 04:49:57 UTC 8,277 KB Current browse context: cs.LG Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .