Diffusion Models as Stochastic Quantization in Lattice Field Theory

arXiv:2309.17082v2 Announce Type: replace-cross
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 …

abstract arxiv cs.lg diffusion diffusion models distribution equation generative hep-lat lattice prior process quantization samples stochastic stochastic process theory type work