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.

该研究通过将生成扩散模型（DMs）与随机量子化与随机微分方程的角度链接，深入探讨了机器学习与晶格场论之间的联系。我们展示了 DMs 可以通过逆转由 Langevin 方程驱动的随机过程的方式进行概念化，从而生成来自初始分布的样本以近似目标分布。通过一个玩具模型，我们强调了 DMs 学习有效动作的能力。此外，我们展示了作为二维 Phi^4 量子晶格场论中生成配置的全局采样器的可行性。

格点场论的生成扩散模型

Generative Diffusion Models for Lattice Field Theory

Recent results have demonstrated that samplers constructed with flow-based
generative models are a promising new approach for configuration generation in
lattice field theory. In this paper, we present a set of methods to construct
flow models for targets with multiple separated modes (i.e. theories with
multiple vacua). We demonstrate the application of these methods to modeling
two-dimensional real scalar field theory in its symmetry-broken phase. In this
context we investigate the performance of different flow-based sampling
algorithms, including a composite sampling algorithm where flow-based proposals
are occasionally augmented by applying updates using traditional algorithms
like HMC.

本文介绍一种构建多模式目标下流水线模型的新方法，应用于二维实标量场理论的对称破缺相建模中，研究不同基于流模型的采样算法的表现，包括一种复合采样算法，其中偶尔会使用传统算法如 HMC 进行更新。

基于流形采样的格点场理论多模型分布抽样

Flow-based sampling for multimodal distributions in lattice field theory

In this work, we demonstrate that applying deep generative machine learning
models for lattice field theory is a promising route for solving problems where
Markov Chain Monte Carlo (MCMC) methods are problematic. More specifically, we
show that generative models can be used to estimate the absolute value of the
free energy, which is in contrast to existing MCMC-based methods which are
limited to only estimate free energy differences. We demonstrate the
effectiveness of the proposed method for two-dimensional $\phi^4$ theory and
compare it to MCMC-based methods in detailed numerical experiments.

本文展示应用深度生成机器学习模型于晶格场论中，可用于解决马尔可夫链蒙特卡罗方法面临问题的前途。特别地，我们展示了生成模型可用于估算自由能的绝对值，这与现有的基于 MCMC 的方法仅估算自由能差异有所不同。我们在二维 $\phi^4$ 理论中展示了所提出方法的有效性，并在详细的数字实验中与基于 MCMC 的方法进行了比较。