Group-Equivariant Diffusion Models for Lattice Field Theory

• URL: http://arxiv.org/abs/2510.26081v1
• Date: Thu, 30 Oct 2025 02:34:01 GMT
• Title: Group-Equivariant Diffusion Models for Lattice Field Theory
• Authors: Octavio Vega, Javad Komijani, Aida El-Khadra, Marina Marinkovic,
• Abstract summary: Near the critical point, Markov Chain Monte Carlo simulations of lattice quantum field theories become increasingly inefficient.<n>In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $phi4$ and $rm U(1)$ lattice field theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\phi^4$ 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.

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