Group-Equivariant Diffusion Models for Lattice Field Theory

arXiv:2510.26081v2 Announce Type: replace-cross Abstract: Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional phi^4 and {rm U}(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global Z_2 reflections, local {rm U}(1) rotations, and periodic translations T. The score networks are trained using an augmented training scheme, which significantly improves sample quality in the simulated field theories. We also demonstrate empirically that our symmetry-aware models outperform generic score networks in sample quality, expressivity, and effective sample size.

Source: arXiv cs.LG | 2026-08-06