Diffusion model for SU(N) gauge theories

TL;DR

This paper develops a diffusion model framework for SU(N) lattice gauge theories, enabling efficient sampling of gauge configurations and comparison with traditional Monte Carlo methods.

Contribution

It introduces a score-matching approach for SU(N) gauge theories, including a Hamiltonian molecular dynamics corrector to improve sampling accuracy.

Findings

Diffusion models can be trained successfully for SU(3) gauge configurations.

The Hamiltonian molecular dynamics corrector enhances sampling quality.

Strategies are proposed to improve sampling efficiency.

Abstract

Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge theories, which can be extended to other Lie groups. We apply the method to SU(3) gauge configurations with the Wilson gauge action in two and four dimensions and assess the quality of the generated samples by comparison with Hybrid Monte Carlo (HMC) simulations. We show that the diffusion models can be successfully trained and applied for sampling the Wilson gauge action. For large values of inverse coupling, accurate reverse-time integration requires predictor-corrector schemes, for which we introduce a corrector based on Hamiltonian molecular dynamics. While the corrector significantly improves sampling quality, it also increases the computational cost. We outline several strategies for improving sampling efficiency.