mlsanityData to 7 Oct 2026

Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories

arXiv 2302.14082 ↗First posted 27 Feb 2023hep-lat cs.LG physics.comp-phcited by 25

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Abstract (arXiv)

We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. Normalizing flows allow for independent sampling. For this reason, it is hoped that they can avoid the tunneling problem of local-update MCMC algorithms for multi-modal distributions. In this work, we first point out that the tunneling problem is also present for normalizing flows but is shifted from the sampling to the training phase of the algorithm. Specifically, normalizing flows often suffer from mode-collapse for which the training process assigns vanishingly low probability mass to relevant modes of the physical distribution. This may result in a significant bias when the flow is used as a sampler in a Markov-Chain or with Importance Sampling. We propose a metric to quantify the degree of mode-collapse and derive a bound on the resulting bias. Furthermore, we propose various mitigation strategies in particular in the context of estimating thermodynamic observables, such as the free energy.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 5 of its 31 references that are in the map. First posted on arXiv 27 Feb 2023.

Builds on

5 of 31 references.

References · 5

  1. 2020Targeted free energy estimation via learned mappingscited by 66
  2. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  3. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  4. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  5. 2021Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Upcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 6; 2025: 9; 2026: 6.

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  1. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  2. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  3. 2024A theoretical perspective on mode collapse in variational inferencecited by 14
  4. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  5. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  6. 2024On learning higher-order cumulants in diffusion modelscited by 10
  7. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  8. 2024Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flowscited by 6
  9. 2024Fast and Unified Path Gradient Estimators for Normalizing Flowscited by 5
  10. 2025Multilevel Generative Samplers for Investigating Critical Phenomenacited by 5
  11. 2025Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimationcited by 5
  12. 2025Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics modelscited by 5
13 more
  1. 2025Hierarchical autoregressive neural networks in three-dimensional statistical systemcited by 3
  2. 2025Path Gradients after Flow Matchingcited by 2
  3. 2025SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flowscited by 2
  4. 2026Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixturescited by 2
  5. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  6. 2025Simulating the Hubbard Model with Equivariant Normalizing Flowscited by 1
  7. 2026AGMA: Adaptive Gaussian Mixture Anchors for Prior-Guided Multimodal Human Trajectory Forecastingcited by 1
  8. 2024Stochastic normalizing flows for Effective String Theorycited by 0
  9. 2025Score-Based Density Estimation from Pairwise Comparisonscited by 0
  10. 2026Variational Autoregressive Networks with probability priorscited by 0
  11. 2026Correlation-Free Transition Path Sampling through Shooting Point Generation Guided by Committor Learningcited by 0
  12. 2026SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flowscited by 0
  13. 2026FUND: Density Flow for Sampling Unnormalised Distributionscited by 0