Spectral Diffusion for Sampling on ${\rm SU}(N)$

TL;DR

This paper develops a diffusion model framework for sampling on the special unitary group ${ m SU}(N)$, enabling efficient and unbiased estimation of lattice field theory observables, with potential applications in quantum chromodynamics.

Contribution

It introduces a novel diffusion modeling approach adapted to the ${ m SU}(N)$ group manifold, advancing sampling techniques in lattice field theory simulations.

Findings

Models accurately reproduce target densities.

Unbiased expectation values are obtained.

Framework paves the way for ${ m SU}(N)$ lattice QCD applications.

Abstract

Although ensemble generation remains a central challenge in lattice field theory simulations, recent advances in generative modeling may offer a path to accelerated sampling in these contexts. In this work, we implement a framework for efficiently training diffusion models acting on ${\rm SU}(N)$ degrees of freedom, adapting the traditional score matching technique to the group manifold. We demonstrate that our models can effectively reproduce several target densities, resulting in precise unbiased expectation values. These results mark a step for diffusion models towards modeling full ${\rm SU}(N)$ lattice field theories, including lattice Quantum Chromodynamics.