mlsanityData to 14 Oct 2026

Normalizing Flows for Probabilistic Modeling and Inference

arXiv 1912.02762 ↗First posted 5 Dec 2019stat.ML cs.LGcited by 1,323

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Cited by 164 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

Key facts. Cited by 1,323 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Dec 2019.

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Citing papers per year: 2021: 142; 2022: 164; 2023: 238; 2024: 245; 2025: 297; 2026: 237.

1,323 papers.

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  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2022Generative Adversarial Networkscited by 5,627
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  4. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  5. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  6. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  7. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 395
  8. 2024Pyramidal Flow Matching for Efficient Video Generative Modelingcited by 366
  9. 2025Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generationcited by 356
  10. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
  11. 2021CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flowscited by 321
  12. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
38 more
  1. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Surveycited by 273
  2. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  3. 2022A Survey on Generative Diffusion Modelcited by 240
  4. 2022Riemannian Score-Based Generative Modellingcited by 219
  5. 2021A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detectioncited by 207
  6. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 197
  7. 2021A Survey on Neural Speech Synthesiscited by 184
  8. 2022Graph neural networks for materials science and chemistrycited by 182
  9. 2021Benchmarking Simulation-Based Inferencecited by 162
  10. 2023Denoising Diffusion Samplerscited by 149
  11. 2022An optimal control perspective on diffusion-based generative modelingcited by 147
  12. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  13. 2023Equivariant flow matchingcited by 135
  14. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  15. 2025Hunyuan3D 2.5: Towards High-Fidelity 3D Assets Generation with Ultimate Detailscited by 125
  16. 2023UniDexGrasp: Universal Robotic Dexterous Grasping via Learning Diverse Proposal Generation and Goal-Conditioned Policycited by 124
  17. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 116
  18. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  19. 2023Improved sampling via learned diffusionscited by 104
  20. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 101
  21. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 101
  22. 2021Independent mechanism analysis, a new concept?cited by 97
  23. 2021Annealed Flow Transport Monte Carlocited by 90
  24. 2024MAISI: Medical AI for Synthetic Imagingcited by 87
  25. 2024Variational Flow Matching for Graph Generationcited by 83
  26. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  27. 2021Predictive Coding: a Theoretical and Experimental Reviewcited by 77
  28. 2023Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamicscited by 72
  29. 2022Causal Machine Learning for Healthcare and Precision Medicinecited by 68
  30. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  31. 2023Functional Flow Matchingcited by 67
  32. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  33. 2023A Comprehensive Review of Data-Driven Co-Speech Gesture Generationcited by 66
  34. 2024Towards Generalizable Tumor Synthesiscited by 65
  35. 2022BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesiscited by 64
  36. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 64
  37. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 63
  38. 2024Riemannian Flow Matching Policy for Robot Motion Learningcited by 63

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