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2023

Diffusion Models as Stochastic Quantization in Lattice Field Theory

Wang, Lingxiao, Aarts, Gert, Zhou, Kai

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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.

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