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This study applies U(1)-equivariant score-based generative models, specifically diffusion methods, to accelerate sampling in the lattice Schwinger model, addressing critical slowing down and topological freezing issues common in traditional MCMC simulations like HMC. By generating unbiased estimates for observables that closely match standard Monte Carlo results, this work demonstrates a viable pathway for integrating advanced machine learning techniques into high-energy physics computations where efficiency is paramount.
Sampling the Schwinger Model with Gauge-Equivariant Diffusion
arXiv:2606.27481v2 Announce Type: replace-cross Abstract: We present a first study of a diffusion-based approach to accelerated sampling of the $N_f = 2$ lattice Schwinger model. Our work is inspired by recent and growing successes in developing such generative models for ensemble generation in LFT to overcome the well-known critical slowing down problem. We train a U(1)-equivariant score-based generative model to sample gauge link configurations from the marginal Schwinger model. By computing model likelihoods, we obtain unbiased estimates for observables that closely match those produced by MCMC simulations. We also demonstrate improvement over HMC as measured qualitatively by a reduction in topological freezing near critical parameters.
Abstract:We present a first study of a diffusion-based approach to accelerated sampling of the $N_f = 2$ lattice Schwinger model. Our work is inspired by recent and growing successes in developing such generative models for ensemble generation in LFT to overcome the well-known critical slowing down problem. We train a U(1)-equivariant score-based generative model to sample gauge link configurations from the marginal Schwinger model. By computing model likelihoods, we obtain unbiased estimates for observables that closely match those produced by MCMC simulations. We also demonstrate improvement over HMC as measured qualitatively by a reduction in topological freezing near critical parameters.
v2: Updated acknowledgements, paper unchanged. Conference paper at PAI 2026. 6 pages, 1 figure
High Energy Physics - Lattice (hep-lat); Strongly Correlated Electrons (cond-mat.str-el); Machine Learning (cs.LG)
arXiv:2606.27481 [hep-lat]
(or arXiv:2606.27481v2 [hep-lat] for this version)
https://doi.org/10.48550/arXiv.2606.27481 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.5281/zenodo.21007460 Focus to learn more DOI(s) linking to related resources
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