mlsanityData to 7 Oct 2026

Annealed Flow Transport Monte Carlo

arXiv 2102.07501 ↗First posted 15 Feb 2021stat.ML cond-mat.stat-mech cs.LGcited by 90

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Cited by 20 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NFs) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NFs which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NFs. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.

Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). Builds on 33 of its 97 references that are in the map. First posted on arXiv 15 Feb 2021.

Builds on

33 of 97 references.

References · 33

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Layer Normalizationcited by 5,579
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  7. 2019Neural Spline Flowscited by 590
  8. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  9. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  10. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  11. 2020Stochastic Normalizing Flowscited by 156
  12. 2017TensorFlow Distributionscited by 105
21 more
  1. 2017Variational Sequential Monte Carlocited by 93
  2. 2017Filtering Variational Objectivescited by 91
  3. 2016Variational inference for Monte Carlo objectivescited by 83
  4. 2020Targeted free energy estimation via learned mappingscited by 66
  5. 2017Auto-Encoding Sequential Monte Carlocited by 64
  6. 2018Importance Weighting and Variational Inferencecited by 55
  7. 2018Hamiltonian Variational Auto-Encodercited by 41
  8. 2016On the Quantitative Analysis of Decoder-Based Generative Modelscited by 40
  9. 2019Accelerated Information Gradient flowcited by 38
  10. 2020Marginal likelihood computation for model selection and hypothesis testing: an extensive reviewcited by 33
  11. 2020An invitation to sequential Monte Carlo samplerscited by 33
  12. 2017Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Netcited by 30
  13. 2020i-flow: High-dimensional Integration and Sampling with Normalizing Flowscited by 26
  14. 2018Improving Explorability in Variational Inference with Annealed Variational Objectivescited by 24
  15. 2015Adaptive importance sampling for control and inferencecited by 23
  16. 2020Evaluating Lossy Compression Rates of Deep Generative Modelscited by 16
  17. 2017Stein Variational Adaptive Importance Samplingcited by 7
  18. 2020MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inferencecited by 7
  19. 2019Diffusion map-based algorithm for Gain function approximation in the Feedback Particle Filtercited by 5
  20. 2020Deep FPF: Gain function approximation in high-dimensional settingcited by 5
  21. 2016Sequential Monte Carlo with transformationscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 10; 2023: 13; 2024: 23; 2025: 25; 2026: 15.

90 papers.

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  1. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  2. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  3. 2023Denoising Diffusion Samplerscited by 144
  4. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  5. 2023Improved sampling via learned diffusionscited by 103
  6. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  7. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  8. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  9. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  10. 2024Particle Denoising Diffusion Samplercited by 63
  11. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  12. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
38 more
  1. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  2. 2024Sequential Controlled Langevin Diffusionscited by 47
  3. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  4. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  5. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  6. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  7. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  8. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  9. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  10. 2024Liouville Flow Importance Samplercited by 25
  11. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  12. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  13. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  14. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
  15. 2023On Sampling with Approximate Transport Mapscited by 20
  16. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  17. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 19
  18. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  19. 2024Score-Optimal Diffusion Schedulescited by 16
  20. 2025Proximal Diffusion Neural Samplercited by 16
  21. 2025FEAT: Free energy Estimators with Adaptive Transportcited by 15
  22. 2021Nested Variational Inferencecited by 14
  23. 2023Improving Gradient-guided Nested Sampling for Posterior Inferencecited by 14
  24. 2023Entropy-based Training Methods for Scalable Neural Implicit Samplercited by 13
  25. 2025Accelerated Parallel Tempering via Neural Transportscited by 13
  26. 2025Progressive Tempering Sampler with Diffusioncited by 13
  27. 2024Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributionscited by 11
  28. 2025Amortized Sampling with Transferable Normalizing Flowscited by 11
  29. 2022Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inferencecited by 10
  30. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  31. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  32. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  33. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
  34. 2023Adaptive Annealed Importance Sampling with Constant Rate Progresscited by 7
  35. 2024Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inferencecited by 7
  36. 2024Importance Corrected Neural JKO Samplingcited by 7
  37. 2025Rethinking Losses for Diffusion Bridge Samplerscited by 7
  38. 2024Practical applications of machine-learned flows on gauge fieldscited by 6

50 most cited of 90 All 90 (JSON)