Diffusion Models as Stochastic Quantization in Lattice Field Theory
Lingxiao Wang Gert Aarts Kai Zhou
In this work, we establish a direct connection between generative diffusion
models (DMs) and stochastic quantization (SQ). The DM is realized by
approximating the reversal of a stochastic process dictated by the Langevin
equation, generating samples from a prior distribution to effectively mimic the
target distribution. Using numerical simulations, we demonstrate that the DM
can serve as a global sampler for generating quantum lattice field
configurations in two-dimensional $\phi^4$ theory. We demonstrate that DMs can
notably reduce autocorrelation times in the Markov chain, especially in the
critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms
experience critical slowing down. The findings can potentially inspire further
advancements in lattice field theory simulations, in particular in cases where
it is expensive to generate large ensembles.