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Diffusion Models as Stochastic Quantization in Lattice Field Theory

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arxiv 2309.17082 v2 pith:75FT5YQ7 submitted 2023-09-29 hep-lat cs.LG

Lingxiao Wang , Gert Aarts , Kai Zhou This is my paper · ORCID
classification hep-latcs.LG
keywords fieldlatticestochastictheorychaincriticaldemonstratediffusion
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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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Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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