发表机构
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China; School of Physics, University of Electronic Science and Technology of China; Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China; Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院; 电子科技大学物理学院; 电子科技大学教育部量子物理与光子量子信息重点实验室; 电子科技大学四川省非经典信息科学基础学科研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于变分自回归网络的离散扩散模型，通过显式马尔可夫跳跃算子实现归一化分布，应用于高维伊辛模型，准确计算热力学量，并与蒙特卡洛采样结合提升低温采样效率。
AI 中文摘要
传统的基于分数的扩散模型学习分数而不表示归一化密度，而可处理的归一化模型同时支持采样和直接似然评估。最近的一种张量网络方法提供了这样的表示，但主要局限于低维晶格。在这里，我们引入了一种离散扩散模型，该模型使用变分自回归网络参数化归一化概率分布。显式的马尔可夫跳跃算子控制前向加噪和反向去噪动力学，将具有归一化分布的离散扩散模型扩展到高维晶格上的自旋系统。我们将此框架应用于二维和三维伊辛模型，涵盖有序、临界和无序区域，准确计算包括自由能、能量和磁化强度在内的热力学量。我们进一步将该框架与蒙特卡洛采样相结合，使用自适应扩散步骤在低温下保持高接受率，同时增强样本多样性。这些结果建立了一个用于具有归一化概率分布的离散扩散模型的神经网络框架。
英文摘要
Conventional score-based diffusion models learn scores without representing normalized densities, whereas tractable normalized models support both sampling and direct likelihood evaluation. A recent tensor-network approach provides such a representation but is largely restricted to low-dimensional lattices. Here we introduce a discrete diffusion model that parameterizes normalized probability distributions using variational autoregressive networks. Explicit Markov jump operators govern the forward noising and reverse denoising dynamics, extending discrete diffusion models with normalized distributions to spin systems on higher-dimensional lattices. We apply this framework to the two- and three-dimensional Ising models across ordered, critical, and disordered regimes, accurately computing thermodynamic quantities including free energy, energy, and magnetization. We further integrate the framework with Monte Carlo sampling, using adaptive diffusion steps to maintain high acceptance rates even at low temperatures while enhancing sample diversity. These results establish a neural-network framework for the discrete diffusion model with normalized probability distributions.
