In this content, we discuss the application of diffusion models in learning inverse renormalization group flows of statistical and quantum field theories. Diffusion models are machine learning models used to generate samples from complex distributions by learning the inverse process of a diffusion process that adds noise to data until it becomes pure noise. We show that nonperturbative renormalization group schemes can be represented as diffusion processes in the field space. Based on this observation, we propose a framework for building machine learning models that learn the inverse process of a specified renormalization group scheme, allowing for the study of field theories. These models can be used as adaptive bridge samplers for lattice field theory. We provide explicit guidelines for comparing results obtained from models associated with different renormalization group schemes. Additionally, we explain how diffusion models can be used in variational methods to find ground states of quantum systems. We apply these methods to numerically find renormalization group flows of interacting statistical field theories. This work not only provides an interpretation of multiscale diffusion models from a machine learning perspective but also offers physically-inspired suggestions for diffusion models with unique properties.
Refining Diffusion Models: A Renormalization Approach (arXiv:2308.12355v1 [hep-th])
