Generative Diffusion Models for Lattice Field Theory
Lingxiao Wang Gert Aarts Kai Zhou
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.