A gauge-equivariant diffusion model samples Schwinger model configurations, yielding unbiased observables matching MCMC and qualitatively less topological freezing than HMC.
Diffusion model for SU(N) gauge theories
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abstract
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.
fields
hep-lat 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A specific noise schedule in Lie-group diffusion models yields linear decay of the Wilson action expectation value versus diffusion time, emerging naturally without an added drift term.
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Sampling the Schwinger Model with Gauge-Equivariant Diffusion
A gauge-equivariant diffusion model samples Schwinger model configurations, yielding unbiased observables matching MCMC and qualitatively less topological freezing than HMC.
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Noise scheduling and linear dynamics in diffusion models on Lie groups
A specific noise schedule in Lie-group diffusion models yields linear decay of the Wilson action expectation value versus diffusion time, emerging naturally without an added drift term.