用扩散模型采样SU(3)规范场，效果接近蒙特卡洛方法。
Diffusion model for SU(N) gauge theories
- 通过隐式得分匹配训练扩散模型，适用于SU(N)规范场。
- 在二维和四维威尔逊作用下生成样本，与HMC结果一致。
- 引入哈密顿分子动力学校正器，提升精度但增加算力开销。
隐式得分匹配为训练扩散模型并从复杂分布中生成高质量样本提供了一种计算高效的途径。本文构建了适用于SU(N)格点规范场的得分匹配框架，可扩展至其他李群。将该方法应用于二维和四维空间中的SU(3)规范构型，采用威尔逊规范作用量，并通过与混合蒙特卡洛（HMC）模拟对比评估生成样本的质量。结果表明，扩散模型可成功训练并用于采样威尔逊规范作用量。在逆耦合较大时，精确的反向积分需采用预测-校正算法，为此提出基于哈密顿分子动力学的校正方案。该校正显著提升采样质量，但也增加了计算成本。文中还提出了若干改进采样效率的策略。
原文摘要 · Abstract (English)
Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge theories, which can be extended to other Lie groups. We apply the method to SU(3) gauge configurations with the Wilson gauge action in two and four dimensions and assess the quality of the generated samples by comparison with Hybrid Monte Carlo (HMC) simulations. We show that the diffusion models can be successfully trained and applied for sampling the Wilson gauge action. For large values of inverse coupling, accurate reverse-time integration requires predictor-corrector schemes, for which we introduce a corrector based on Hamiltonian molecular dynamics. While the corrector significantly improves sampling quality, it also increases the computational cost. We outline several strategies for improving sampling efficiency.
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