Diffusion Models for Sampling Near Criticality in Lattice Field Theories
Yang-yang Tan🇨🇳 · Gert Aarts🇬🇧 · Diaa E. Habibi🇬🇧 · Biagio Lucini🇬🇧 · Lingxiao Wang🇯🇵
We investigate generative diffusion models as denoising samplers for two- and three-dimensional lattice theory across the symmetric, near-critical, and broken phases. Validated against ensembles generated by Fourier-accelerated HMC combined with Wolff cluster updates, the reverse-SDE sampler reproduces scalar observables and the momentum-space propagator , with residual bias concentrated in the zero-mode and, in three dimensions, the action density. We introduce two local diagnostics and an HMC-referenced effective sample size (ESS), which probe the learned drift directly, through a Metropolis-adjusted Langevin acceptance rate, and through observable-level bias and variance. Exploiting a fully convolutional architecture with weights shared across different volumes (), we show that cross-volume training transfers to unseen sizes, matching or slightly improving in-distribution training in the two-dimensional symmetric and broken phases. A three-dimensional model trained on reproduces the propagator and most scalar observables at the unseen lattice size across the phase diagram, with the residual susceptibility excess in the broken phase as the main exception, and improves several critical observables relative to in-distribution training. This establishes cross-volume generalization as a viable mechanism for large-volume sampling, and the score learned from many cheap small-lattice configurations transfers to the target volume without retraining.