We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.

翻译：我们证明，规范等变扩散模型能够通过Metropolis调整退火Langevin算法（MAALA）精确建模非阿贝尔格点规范理论的物理特性，并以二维U(2)和SU(2)规范理论的计算为例进行说明。我们的网络架构基于格点规范等变卷积神经网络（L-CNNs），该架构严格遵循格点上的局域与全局对称性。所有模型均在传统蒙特卡洛方法生成的单一系综上进行训练。通过对不同尺寸的Wilson圈以及拓扑敏感度的研究，我们发现扩散模型在推广至更大反耦合常数和格点尺寸时表现出卓越的泛化能力，在保持较高接受率的同时，精度损失可忽略不计。