Generative Diffusion Models for Lattice Field Theory
This work addresses the problem of sampling configurations in lattice field theory for physicists, presenting a novel application of diffusion models but is incremental in adapting existing methods to a new domain.
The study connects generative diffusion models to lattice field theory by showing they can be conceptualized as reversing a Langevin equation process, and demonstrates their capability to learn effective actions in a toy model and act as a global sampler for generating configurations in a two-dimensional quantum lattice field theory.
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 $φ^4$ quantum lattice field theory.