{"ID":2847838,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.26081","arxiv_id":"2510.26081","title":"Group-Equivariant Diffusion Models for Lattice Field Theory","abstract":"Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $φ^4$ and ${\\rm U}(1)$ lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global $\\mathbb{Z}_2$ reflections, local ${\\rm U}(1)$ rotations, and periodic translations $\\mathbb{T}$. The score networks are trained using an augmented training scheme, which significantly improves sample quality in the simulated field theories. We also demonstrate empirically that our symmetry-aware models outperform generic score networks in sample quality, expressivity, and effective sample size.","short_abstract":"Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $φ^4$ and ${\\rm U...","url_abs":"https://arxiv.org/abs/2510.26081","url_pdf":"https://arxiv.org/pdf/2510.26081v1","authors":"[\"Octavio Vega\",\"Javad Komijani\",\"Aida El-Khadra\",\"Marina Marinkovic\"]","published":"2025-10-30T02:34:01Z","proceeding":"hep-lat","tasks":"[\"hep-lat\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}