Diffusion models for lattice gauge field simulations

We develop diffusion models for lattice gauge theories which build on the concept of stochastic quantization. This framework is applied to $U(1)$ gauge theory in $1+1$ dimensions. We show that a model trained at a small inverse coupling can be effectively transferred to larger inverse coupling without encountering issues related to topological freezing. Additionally, the model is capable of estimating Wilson loops and topological quantities with explicit physics conditions without additional training, demonstrating its potential for efficient lattice gauge theory simulations.