标题： 晶格场论的生成扩散模型 显示英文标题

标题： Generative Diffusion Models for Lattice Field Theory

摘要： 本研究从随机微分方程的角度出发，探讨了机器学习与格点场论之间的联系，将生成扩散模型（DMs）与随机量子化联系起来。 我们表明， DMs 可以通过逆转由朗之万方程驱动的随机过程来概念化，从而从初始分布产生样本以逼近目标分布。 在玩具模型中，我们强调了 DMs 学习有效作用的能力。 此外，我们证明了它可以用作二维 $\phi^4$ 量子格点场论中生成构型的全局采样器的可行性。 显示英文摘要

摘要： This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We show that DMs can be conceptualized by reversing a stochastic process driven by the Langevin equation, which then produces samples from an initial distribution to approximate the target distribution. In a toy model, we highlight the capability of DMs to learn effective actions. Furthermore, we demonstrate its feasibility to act as a global sampler for generating configurations in the two-dimensional $\phi^4$ quantum lattice field theory.