Diffusion Models as Stochastic Quantization in Lattice Field Theory

• URL: http://arxiv.org/abs/2309.17082v2
• Date: Thu, 9 May 2024 00:56:24 GMT
• Title: Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Authors: Lingxiao Wang, Gert Aarts, Kai Zhou,
• Abstract summary: We establish a direct connection between generative diffusion models (DMs) and quantization (SQ). The DM is realized by approximating the reversal of a process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo algorithms experience critical slowing down.
• Score: 7.221319972004889
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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