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<p>Near the critical point, Markov Chain Monte Carlo simulations of lattice quantum field theories 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 <i>ϕ</i><sup>4</sup> and U(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global <i>ℤ</i><sub>2</sub> reflections, local U(1) rotations, and periodic translations <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="double-struck">T</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathbbm{T} \)</EquationSource> </InlineEquation>. The score networks are trained using an augmented training scheme, which improves sample quality in the simulated field theories. We also demonstrate that our symmetry-aware models outperform generic score networks in expressivity and effective sample size.</p>

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Group-equivariant diffusion models for lattice field theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月23日

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  • Octavio Vega,
  • Javad Komijani,
  • Aida El-Khadra,
  • Marina Marinkovic

摘要

Near the critical point, Markov Chain Monte Carlo simulations of lattice quantum field theories 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 ϕ4 and U(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global ℤ2 reflections, local U(1) rotations, and periodic translations T \( \mathbbm{T} \) . The score networks are trained using an augmented training scheme, which improves sample quality in the simulated field theories. We also demonstrate that our symmetry-aware models outperform generic score networks in expressivity and effective sample size.