Generative Diffusion Models for Lattice Field Theory

TL;DR

This paper explores how generative diffusion models can be applied to lattice field theory, linking stochastic processes with machine learning to generate quantum field configurations effectively.

Contribution

It introduces a novel connection between diffusion models and stochastic quantization, demonstrating their application in sampling lattice field configurations.

Findings

Diffusion models can learn effective actions in toy models.

Feasibility of using DMs as global samplers for 2D quantum field theory.

Potential to improve sampling methods in lattice field theory.

Abstract

This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We show that DMs can be conceptualized by reversing a stochastic process driven by the Langevin equation, which then produces samples from an initial distribution to approximate the target distribution. In a toy model, we highlight the capability of DMs to learn effective actions. Furthermore, we demonstrate its feasibility to act as a global sampler for generating configurations in the two-dimensional $\phi^4$ quantum lattice field theory.