Diffusion Models for Ensemble Generation in Lattice Gauge Theory

Simulating lattice quantum field theories (LQFT) is computationally challenging, and generating physical ensembles from high-dimensional probability densities is a major bottleneck. Markov Chain Monte Carlo (MCMC) methods suffer from long autocorrelation times and require extensive computational resources to sample field configurations from arbitrarily complex probability distributions, particularly for non-Abelian gauge groups such as SU(N). In this work, we leverage diffusion models to generate gauge field configurations, represented by special unitary matrices. We parameterize SU(N) matrices by their Lie algebra generators and diffuse over the coefficients of the generators, enabling exploration of the configurations in Euclidean space. Another option we explore is diffusing the Euler angle parameters of SU(N) matrices. Additionally, we showcase preliminary results using a novel technique we introduce termed spectral diffusion, which diffuses the eigenvalues of field operators to produce ensembles. Our model is evaluated by computing observables, including Wilson loops and Creutz ratios, to benchmark against traditional MCMC-derived ensembles. We discuss the scalability of this approach to LQFT simulations that diversifies the avenues for applying deep generative models in high-energy physics.