mlsanityData to 7 Oct 2026

Variational Inference with Normalizing Flows

arXiv 1505.05770 ↗First posted 21 May 2015stat.ML cs.AI cs.LGcited by 2,161

Not on the map. Why?

Cited by 348 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Key facts. Cited by 2,161 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 May 2015.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2018: 1; 2019: 2; 2020: 3; 2021: 345; 2022: 346; 2023: 452; 2024: 388; 2025: 372; 2026: 252.

2,161 papers.

Sort:

By area:

  1. 2020Denoising Diffusion Implicit Modelscited by 9,655
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  3. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  4. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  5. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  6. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  8. 2023PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesiscited by 854
  9. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  10. 2021Generalized Out-of-Distribution Detection: A Surveycited by 796
  11. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  12. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
38 more
  1. 2021DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulationcited by 640
  2. 2021Score-based Generative Modeling in Latent Spacecited by 634
  3. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  4. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
  5. 2025Mean Flows for One-step Generative Modelingcited by 524
  6. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  7. 20233DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Modelscited by 449
  8. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  9. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 384
  10. 2023Shap-E: Generating Conditional 3D Implicit Functionscited by 379
  11. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
  12. 2021AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecastingcited by 327
  13. 2021GFlowNet Foundationscited by 286
  14. 2021How to Train Your Energy-Based Modelscited by 271
  15. 2021Generating Images with Sparse Representationscited by 262
  16. 2023SimpleNet: A Simple Network for Image Anomaly Detection and Localizationcited by 256
  17. 2021CLIP-Forge: Towards Zero-Shot Text-to-Shape Generationcited by 254
  18. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  19. 2023Using Human Feedback to Fine-tune Diffusion Models without Any Reward Modelcited by 246
  20. 2022BigVGAN: A Universal Neural Vocoder with Large-Scale Trainingcited by 245
  21. 2022A Survey on Generative Diffusion Modelcited by 238
  22. 2021FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flowscited by 225
  23. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
  24. 2024Diffusion Model-Based Image Editing: A Surveycited by 212
  25. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  26. 2023InterGen: Diffusion-based Multi-human Motion Generation under Complex Interactionscited by 205
  27. 2018Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learningcited by 203
  28. 2021PIRenderer: Controllable Portrait Image Generation via Semantic Neural Renderingcited by 202
  29. 2022Versatile Diffusion: Text, Images and Variations All in One Diffusion Modelcited by 199
  30. 2023Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion modelscited by 199
  31. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  32. 2023XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchiescited by 183
  33. 2021A Survey on Neural Speech Synthesiscited by 182
  34. 2023InterDiff: Generating 3D Human-Object Interactions with Physics-Informed Diffusioncited by 181
  35. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  36. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  37. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  38. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171

50 most cited of 2,161 All 2,161 (JSON)