# Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

arXiv: https://arxiv.org/abs/2601.19552 · HTML: https://mlsanity.com/paper/2601.19552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 1 of its 67 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Placed in

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

## Builds on (most cited first, 1 of 1)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)

## Built on by (most cited first, 4 of 4)

- [Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories](https://mlsanity.com/paper/2605.03901/) (2026)
- [Are We Ready for AI-Driven Discovery? AI Verification Before the Next Fundamental Physics Breakthrough](https://mlsanity.com/paper/2607.10039/) (2026)
- [Machine learning for four-dimensional SU(3) lattice gauge theories](https://mlsanity.com/paper/2604.12416/) (2026)
- [Data Free Training of Diffusion Models for Lattice Field Theories](https://mlsanity.com/paper/2610.18863/) (2026)

## Abstract (arXiv)

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.