Diffusion Models as Stochastic Quantization in Lattice Field Theory
This work addresses a bottleneck in lattice field theory simulations, particularly for expensive ensemble generation, by applying an existing machine learning method to a new domain.
The authors tackled the problem of critical slowing down in Markov Chain Monte-Carlo simulations for lattice field theory by using diffusion models as global samplers, demonstrating a notable reduction in autocorrelation times in the critical region of two-dimensional φ⁴ theory.
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 $φ^4$ 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.