Group-equivariant diffusion models for lattice field theory

A bstract Near the critical point, Markov Chain Monte Carlo simulations of lattice quantum field theories 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 ϕ 4 and U(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global ℤ 2 reflections, local U(1) rotations, and periodic translations $$ \mathbbm{T} $$ T . The score networks are trained using an augmented training scheme, which improves sample quality in the simulated field theories. We also demonstrate that our symmetry-aware models outperform generic score networks in expressivity and effective sample size.