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Workshop: NeurIPS 2023 Workshop: Machine Learning and the Physical Sciences

Generative Diffusion Models for Lattice Field Theory

Lingxiao Wang · Gert Aarts · Kai Zhou

Abstract: This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization (SQ), from a stochastic differential equation(SDE) 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.

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