mlsanityData to 14 Oct 2026

Neural Autoregressive Flows

arXiv 1804.00779 ↗First posted 3 Apr 2018cs.LG stat.MLcited by 208

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Abstract (arXiv)

Normalizing flows and autoregressive models have been successfully combined to produce state-of-the-art results in density estimation, via Masked Autoregressive Flows (MAF), and to accelerate state-of-the-art WaveNet-based speech synthesis to 20x faster than real-time, via Inverse Autoregressive Flows (IAF). We unify and generalize these approaches, replacing the (conditionally) affine univariate transformations of MAF/IAF with a more general class of invertible univariate transformations expressed as monotonic neural networks. We demonstrate that the proposed neural autoregressive flows (NAF) are universal approximators for continuous probability distributions, and their greater expressivity allows them to better capture multimodal target distributions. Experimentally, NAF yields state-of-the-art performance on a suite of density estimation tasks and outperforms IAF in variational autoencoders trained on binarized MNIST.

Key facts. Cited by 208 papers in the map (data through 14 Oct 2026). First posted on arXiv 3 Apr 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 51; 2022: 51; 2023: 33; 2024: 30; 2025: 30; 2026: 13.

208 papers.

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  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  3. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  4. 2023A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPTcited by 224
  5. 2021A Survey on Neural Speech Synthesiscited by 184
  6. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 183
  7. 2022Riemannian Diffusion Modelscited by 122
  8. 2021Independent mechanism analysis, a new concept?cited by 97
  9. 2022Deep End-to-end Causal Inferencecited by 95
  10. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  11. 2021Diffusion Normalizing Flowcited by 77
  12. 2021Flow-based Kernel Prior with Application to Blind Super-Resolutioncited by 74
38 more
  1. 2021Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescalingcited by 73
  2. 2021Generating Smooth Pose Sequences for Diverse Human Motion Predictioncited by 66
  3. 2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
  4. 2021Smooth Normalizing Flowscited by 53
  5. 2021Copula Flows for Synthetic Data Generationcited by 35
  6. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  7. 2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
  8. 2023Autoregressive Conditional Neural Processescited by 33
  9. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  10. 2022Universal approximation property of invertible neural networkscited by 30
  11. 2021Implicit Normalizing Flowscited by 28
  12. 2021iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Codercited by 26
  13. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 26
  14. 2022Empirical Analysis of Model Selection for Heterogeneous Causal Effect Estimationcited by 25
  15. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  16. 2021Local-Global MCMC kernels: the best of both worldscited by 22
  17. 2023Distribution learning via neural differential equations: a nonparametric statistical perspectivecited by 22
  18. 2021FloMo: Tractable Motion Prediction with Normalizing Flowscited by 21
  19. 2022Differentiable Causal Discovery Under Latent Interventionscited by 21
  20. 2022Normalizing Flows for Interventional Density Estimationcited by 21
  21. 2024Sample, estimate, aggregate: A recipe for causal discovery foundation modelscited by 21
  22. 2021CausalAF: Causal Autoregressive Flow for Safety-Critical Driving Scenario Generationcited by 20
  23. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 20
  24. 2024Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directionscited by 20
  25. 2025Towards Hierarchical Rectified Flowcited by 20
  26. 2022Optimal transport for causal discoverycited by 19
  27. 2021A deep generative model for probabilistic energy forecasting in power systems: normalizing flowscited by 18
  28. 2024On the Universality of Volume-Preserving and Coupling-Based Normalizing Flowscited by 18
  29. 2025FARMER: Flow AutoRegressive Transformer over Pixelscited by 18
  30. 2022Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularizationcited by 17
  31. 2022Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Schemecited by 17
  32. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  33. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 17
  34. 2021Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Ratescited by 16
  35. 2022Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flowscited by 16
  36. 2022Flow-based Recurrent Belief State Learning for POMDPscited by 16
  37. 2021Autoregressive Quantile Flows for Predictive Uncertainty Estimationcited by 15
  38. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15

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