# Diffusion Models for Cayley Graphs

arXiv: https://arxiv.org/abs/2503.05558 · HTML: https://mlsanity.com/paper/2503.05558/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 4 of 4)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Solving the Rubik's Cube Without Human Knowledge](https://mlsanity.com/paper/1805.07470/) (2018)
- [What makes math problems hard for reinforcement learning: a case study](https://mlsanity.com/paper/2408.15332/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning the Graphical Nature of Symmetries](https://mlsanity.com/paper/2607.12026/) (2026)

## Abstract (arXiv)

We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems in the framework of diffusion models. The exploration of the graph is carried out by the forward process, while finding the target nodes is done by the inverse backward process. This systematizes the discussion and suggests many generalizations. To improve exploration, we propose a ``reversed score'' ansatz which substantially improves over previous comparable algorithms.