用扩散模型学习复数朗之万过程采样的分布，解决量子物理中的符号问题。
Combining complex Langevin dynamics with score-based and energy-based diffusion models
- 用生成式扩散模型学习复数配置空间中的采样分布
- 分数基与能量基扩散模型在建模复杂朗之万过程上表现相当
- 适合研究量子场论、统计物理中存在符号问题的系统
由于作用量或玻尔兹曼权函数为复数导致符号问题的理论，有时可通过复化配置空间中的随机过程进行数值求解。然而，该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AI中，扩散模型可从数据中学习分布或其对数导数。本文探索了扩散模型学习复数朗之万过程采样分布的能力，比较了分数基与能量基扩散模型的表现，并推测其潜在应用。
原文摘要 · Abstract (English)
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.
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