标题： 将复数Langevin动力学与基于评分和基于能量的扩散模型相结合 显示英文标题

标题： Combining complex Langevin dynamics with score-based and energy-based diffusion models

摘要： 由于复数作用量或玻尔兹曼权重导致符号问题的理论，有时可以使用复化配置空间中的随机过程进行数值求解。 然而，这种复数朗之万过程实际采样的概率分布事先未知且难以理解。 在生成式人工智能中，扩散模型可以从数据中学习分布或其对数导数。 我们探讨扩散模型学习复数朗之万过程采样分布的能力，比较基于得分的和基于能量的扩散模型，并推测可能的应用。 显示英文摘要

摘要： 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.