Diffusion Models as Stochastic Quantization in Lattice Field Theory

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 ${\varphi }^4$ 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.

30 pages, 15 figures. The open code can be found at https://github.com/Anguswlx/DMasSQ

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• Lattice simulations of real-time quantum fields
• Stochastic quantization at finite chemical potential
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• Toward a foundation model for heavy-ion collision experiments based on point-cloud diffusion
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limit
• Reconstruction of Gravitational Form Factors using Generative Machine Learning
• Diffusion Models for SU(2) Lattice Gauge Theory in Two Dimensions
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes
• Variational Neural Network Approach to QFT in the Field Basis
• Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization
• Combining complex Langevin dynamics with score-based and energy-based diffusion models
• Group-Equivariant Diffusion Models for Lattice Field Theory