Combining complex Langevin dynamics with score-based and energy-based diffusion models
This work addresses a challenge in computational physics for researchers dealing with complex actions, but it appears incremental as it speculates on applications without concrete results.
The paper tackled the problem of understanding the probability distributions sampled by complex Langevin processes, which are used to solve theories with sign problems, by exploring the ability of diffusion models to learn these distributions, comparing score-based and energy-based approaches.
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications.