mlsanityData to 7 Oct 2026

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

arXiv 1904.12072 ↗First posted 26 Apr 2019hep-lat cond-mat.dis-nn cond-mat.stat-mechcited by 147

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Cited by 24 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for φ4 theory in two dimensions.

Key facts. Cited by 147 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Apr 2019.

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Citing papers per year: 2021: 19; 2022: 25; 2023: 21; 2024: 24; 2025: 31; 2026: 27.

147 papers.

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  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  3. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  4. 2021A Living Review of Machine Learning for Particle Physicscited by 77
  5. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  6. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  7. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  8. 2021Smooth Normalizing Flowscited by 52
  9. 2021Machine Learning in the Search for New Fundamental Physicscited by 50
  10. 2024Improved off-policy training of diffusion samplerscited by 47
  11. 2021Variational Neural Annealingcited by 45
  12. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
38 more
  1. 2022Universal approximation property of invertible neural networkscited by 30
  2. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  3. 2022Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inferencecited by 28
  4. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  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. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  10. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  11. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  12. 2021Local-Global MCMC kernels: the best of both worldscited by 21
  13. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 21
  14. 2023On Sampling with Approximate Transport Mapscited by 20
  15. 2024On the Universality of Volume-Preserving and Coupling-Based Normalizing Flowscited by 18
  16. 2024Efficient mapping of phase diagrams with conditional Boltzmann Generatorscited by 18
  17. 2021Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networkscited by 17
  18. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  19. 2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 17
  20. 2021Ab-initio study of interacting fermions at finite temperature with neural canonical transformationcited by 16
  21. 2023Renormalizing Diffusion Modelscited by 16
  22. 2023Controlling Continuous Relaxation for Combinatorial Optimizationcited by 16
  23. 2021Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methodscited by 15
  24. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  25. 2024Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Modelscited by 14
  26. 2024A theoretical perspective on mode collapse in variational inferencecited by 14
  27. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  28. 2021Differentiable Physics: A Position Piececited by 12
  29. 2022Hierarchical autoregressive neural networks for statistical systemscited by 12
  30. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  31. 2021Latent Space Refinement for Deep Generative Modelscited by 10
  32. 2021Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulationscited by 10
  33. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  34. 2022Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inferencecited by 10
  35. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  36. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion modelscited by 10
  37. 2024On learning higher-order cumulants in diffusion modelscited by 10
  38. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9

50 most cited of 147 All 147 (JSON)