Physics-Conditioned Diffusion Models for Lattice Gauge Theory

TL;DR

This paper introduces physics-conditioned diffusion models for lattice gauge theory simulation, enabling efficient, exact sampling across different parameters and lattice sizes, surpassing traditional methods in topological quantity sampling.

Contribution

The authors develop a novel diffusion-based sampler incorporating stochastic quantization, allowing extrapolation across coupling constants and lattice sizes without retraining.

Findings

Model trained at small inverse coupling extrapolates to larger regions.

Sampler can handle different lattice sizes without retraining.

More efficient sampling of topological quantities than traditional algorithms.

Abstract

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.