Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests

Abstract

Gauge-equivariant diffusion models can be used to generate ensembles of field configurations in non-abelian lattice gauge theories. Previously, we demonstrated the feasibility of modeling these theories by combining L-CNN-based diffusion models with the Metropolis-adjusted annealed Langevin algorithm (MAALA). Here we focus on the underlying analytical framework. In particular, we present a rigorous derivation of the reverse-time stochastic differential equation on the group manifold, discuss the gauge invariance of the denoising loss function, and provide extensive numerical benchmarks regarding the scaling behavior with respect to the lattice volume and the inverse coupling $β$. Full analytical expressions for arbitrarily sized Wilson loops and the topological charge susceptibility during the forward process are given as well.