Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests
Abstract
Gauge-equivariant diffusion models can be used to generate ensembles of field configurations in non-abelian lattice gauge theories. Previously, we demonstrated the feasibility of modeling these theories by combining L-CNN-based diffusion models with the Metropolis-adjusted annealed Langevin algorithm (MAALA). Here we focus on the underlying analytical framework. In particular, we present a rigorous derivation of the reverse-time stochastic differential equation on the group manifold, discuss the gauge invariance of the denoising loss function, and provide extensive numerical benchmarks regarding the scaling behavior with respect to the lattice volume and the inverse coupling β. Full analytical expressions for arbitrarily sized Wilson loops and the topological charge susceptibility during the forward process are given as well.
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BibTeX
@misc{aarts2026generalizable,
title = {{Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests}},
author = {Gert Aarts and Diaa E. Habibi and Andreas Ipp and David I. Müller and Thomas R. Ranner and Lingxiao Wang and Wei Wang and Qianteng Zhu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03530},
eprint = {2611.03530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03530},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests
AU - Gert Aarts
AU - Diaa E. Habibi
AU - Andreas Ipp
AU - David I. Müller
AU - Thomas R. Ranner
AU - Lingxiao Wang
AU - Wei Wang
AU - Qianteng Zhu
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03530
UR - https://arxiv.org/abs/2611.03530
AB - Gauge-equivariant diffusion models can be used to generate ensembles of field configurations in non-abelian lattice gauge theories. Previously, we demonstrated the feasibility of modeling these theories by combining L-CNN-based diffusion models with the Metropolis-adjusted annealed Langevin algorithm (MAALA). Here we focus on the underlying analytical framework. In particular, we present a rigorous derivation of the reverse-time stochastic differential equation on the group manifold, discuss the gauge invariance of the denoising loss function, and provide extensive numerical benchmarks regarding the scaling behavior with respect to the lattice volume and the inverse coupling β. Full analytical expressions for arbitrarily sized Wilson loops and the topological charge susceptibility during the forward process are given as well.
ER -