mlsanityData to 7 Oct 2026

Stochastic normalizing flows as non-equilibrium transformations

arXiv 2201.08862 ↗First posted 21 Jan 2022hep-lat cond-mat.stat-mech cs.LGcited by 25

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Abstract (arXiv)

Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of stochastic normalizing flows, in which neural-network layers are combined with Monte Carlo updates, is the same that underlies out-of-equilibrium simulations based on Jarzynski's equality, which have been recently deployed to compute free-energy differences in lattice gauge theories. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 19 of its 101 references that are in the map. First posted on arXiv 21 Jan 2022.

Builds on

19 of 101 references.

References · 19

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  5. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  7. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  8. 2020Sampling using SU(N) gauge equivariant flowscited by 83
  9. 2018Neural Network Renormalization Groupcited by 48
  10. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  11. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  12. 2021Flow-based sampling for fermionic lattice field theoriescited by 27
7 more
  1. 2021Flow-based sampling for multimodal and extended-mode distributions in lattice field theorycited by 25
  2. 2021Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flowscited by 24
  3. 2017QCD-Aware Recursive Neural Networks for Jet Physicscited by 22
  4. 2021Quantum field-theoretic machine learningcited by 16
  5. 2020Towards Novel Insights in Lattice Field Theory with Explainable Machine Learningcited by 12
  6. 2019Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learningcited by 3
  7. 2020Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamicscited by 3

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Citing papers per year: 2022: 2; 2023: 4; 2024: 7; 2025: 8; 2026: 4.

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  1. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  2. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  5. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  6. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  7. 2024On learning higher-order cumulants in diffusion modelscited by 10
  8. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  9. 2024Practical applications of machine-learned flows on gauge fieldscited by 6
  10. 2024Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flowscited by 6
  11. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  12. 2025Multilevel Generative Samplers for Investigating Critical Phenomenacited by 5
13 more
  1. 2022Estimating the Euclidean quantum propagator with deep generative modeling of Feynman pathscited by 3
  2. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  3. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  4. 2025SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flowscited by 2
  5. 2026Toward Scalable Normalizing Flows for the Hubbard Modelcited by 2
  6. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  7. 2025Simulating the Hubbard Model with Equivariant Normalizing Flowscited by 1
  8. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  9. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  10. 2024Stochastic normalizing flows for Effective String Theorycited by 0
  11. 2025Studying Effective String Theory using deep generative modelscited by 0
  12. 2026Machine learning for four-dimensional SU(3) lattice gauge theoriescited by 0
  13. 2026Accurate Sampling from Diffusion Modelscited by 0