Improvement of Heatbath Algorithm in LFT using Generative models

The Heatbath Algorithm is commonly used for sampling in local lattice field theories, but performing exact updates or sampling from the local density is challenging when dealing with continuous variables. Heatbath methods rely on rejection-based sampling at each site, which can suffer from low acceptance rates if the proposal distribution is not optimally chosen—a non-trivial task. In this work, we propose a novel, straightforward approach for generating proposals at each lattice site for the $\phi^4$ and XY models using generative AI models. This method learns a conditional local distribution, without requiring training samples from the target, conditioned on both neighboring sites and action parameter values.