mlsanityData to 14 Oct 2026

Introduction to Normalizing Flows for Lattice Field Theory

arXiv 2101.08176 ↗First posted 20 Jan 2021hep-lat cond-mat.stat-mech cs.LGcited by 35

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Abstract (arXiv)

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428, and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). Builds on 8 of its 27 references that are in the map. First posted on arXiv 20 Jan 2021.

Builds on

8 of 27 references.

References · 8

  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  2. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  3. 2020Stochastic Normalizing Flowscited by 157
  4. 2020Riemannian Continuous Normalizing Flowscited by 145
  5. 2015How (not) to Train your Generative Model: Scheduled Sampling, Likelihood, Adversary?cited by 78
  6. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  7. 2020Neural Ordinary Differential Equations on Manifoldscited by 31
  8. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 28

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 9; 2022: 8; 2023: 10; 2024: 3; 2025: 3; 2026: 2.

35 papers.

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  1. 2023SE(3) diffusion model with application to protein backbone generationcited by 219
  2. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  3. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  4. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  5. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  6. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  7. 2021Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flowscited by 24
  8. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  9. 2021A deep generative model for probabilistic energy forecasting in power systems: normalizing flowscited by 18
  10. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  11. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 11
  12. 2021Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulationscited by 10
23 more
  1. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion modelscited by 10
  2. 2023Sampling Multimodal Distributions with the Vanilla Score: Benefits of Data-Based Initializationcited by 10
  3. 2021Deep Learning Hamiltonian Monte Carlocited by 7
  4. 2023Fluctuation without dissipation: Microcanonical Langevin Monte Carlocited by 7
  5. 2021Machine learning spectral functions in lattice QCDcited by 6
  6. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  7. 2022Simulating first-order phase transition with hierarchical autoregressive networkscited by 5
  8. 2024Fast and Unified Path Gradient Estimators for Normalizing Flowscited by 5
  9. 2023Mutual information of spin systems from autoregressive neural networkscited by 4
  10. 2021Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modelingcited by 3
  11. 2021LeapfrogLayers: A Trainable Framework for Effective Topological Samplingcited by 3
  12. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  13. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  14. 2021A Probabilistic Forecast-Driven Strategy for a Risk-Aware Participation in the Capacity Firming Market: extended versioncited by 2
  15. 2022Gradient estimators for normalising flowscited by 2
  16. 2023Training normalizing flows with computationally intensive target probability distributionscited by 2
  17. 2025Neural Triangular Transport Maps: A New Approach Towards Sampling in Lattice QCDcited by 2
  18. 2022Deformations of Boltzmann Distributionscited by 1
  19. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  20. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  21. 2021Lattice gauge symmetry in neural networkscited by 0
  22. 2026Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theoriescited by 0
  23. 2026Accurate Sampling from Diffusion Modelscited by 0