mlsanityData to 14 Oct 2026

Group-Equivariant Diffusion Models for Lattice Field Theory

arXiv 2510.26081 ↗First posted 30 Oct 2025hep-lat cs.LGcited by 3

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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 φ4 and rm U(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global mathbbZ2 reflections, local rm U(1) rotations, and periodic translations mathbbT. 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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 51 of its 124 references that are in the map. First posted on arXiv 30 Oct 2025.

Builds on

51 of 124 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theory8 Feb
  2. 2024Diffusion models learn distributions generated by complex Langevin dynamics2 Dec
  3. 2023Generative Diffusion Models for Lattice Field Theory6 Nov
  4. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theory29 Sep
  5. 2022Diffusion Models in Vision: A Survey10 Sep
  6. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  8. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  9. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  10. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesis29 Nov
  11. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 38

  1. 2017Attention Is All You Needcited by 60,361
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  7. 2022Generative Adversarial Networkscited by 5,627
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2018Neural Ordinary Differential Equationscited by 3,779
  10. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,614
  11. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  12. 2015Variational Inference with Normalizing Flowscited by 2,170
26 more
  1. 2016Density estimation using Real NVPcited by 2,042
  2. 2018Group Normalizationcited by 1,524
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  4. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 313
  5. 2020Stochastic Normalizing Flowscited by 157
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  7. 2020Normalizing Flows on Tori and Spherescited by 117
  8. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
  9. 2020Adversarial score matching and improved sampling for image generationcited by 96
  10. 2020Sampling using SU(N) gauge equivariant flowscited by 84
  11. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  12. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  13. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  14. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 31
  15. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  16. 2024Diffusion Models in textitDe Novo Drug Designcited by 26
  17. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  18. 2023Normalizing flows for lattice gauge theory in arbitrary space-time dimensioncited by 23
  19. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  20. 2022Flow-based sampling in the lattice Schwinger model at criticalitycited by 20
  21. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  22. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  23. 2024Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theorycited by 10
  24. 2023Generative models for scalar field theories: how to deal with poor scaling?cited by 6
  25. 2024Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flowscited by 6
  26. 2025Normalizing flows for SU(N) gauge theories employing singular value decompositioncited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Capturing the Topological Phase Transition and Thermodynamics of the 2D XY Model via Manifold-Aware Score-Based Generative Modelingcited by 0
  2. 2026Sampling the Schwinger Model with Gauge-Equivariant Diffusioncited by 0
  3. 2026Machine learning for the LHC physics program: a 2025-2026 stocktakecited by 0

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  2. 2026Data Free Training of Diffusion Models for Lattice Field Theories
  3. 2026Diffusion model for SU(N) gauge theories
  4. 2023Renormalizing Diffusion Models
  5. 2026Diffusion-warm sampling of the XY model enables fast thermalization at scale
  6. 2026Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory
  7. 2026Discrete Diffusion Models via Evolving Variational Autoregressive Networks
  8. 2024Understanding Diffusion Models by Feynman's Path Integral