mlsanityData to 7 Oct 2026

Block Neural Autoregressive Flow

arXiv 1904.04676 ↗First posted 9 Apr 2019stat.ML cs.LGcited by 62

Not on the map. Why?

Abstract (arXiv)

Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for parametrization is needed. We propose block neural autoregressive flow (B-NAF), a much more compact universal approximator of density functions, where we model a bijection directly using a single feed-forward network. Invertibility is ensured by carefully designing each affine transformation with block matrices that make the flow autoregressive and (strictly) monotone. We compare B-NAF to NAF and other established flows on density estimation and approximate inference for latent variable models. Our proposed flow is competitive across datasets while using orders of magnitude fewer parameters.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Apr 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 17; 2022: 14; 2023: 7; 2024: 12; 2025: 8; 2026: 4.

62 papers.

Sort:

By area:

  1. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  2. 2023A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPTcited by 221
  3. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
  4. 2024Normalizing Flows are Capable Generative Modelscited by 89
  5. 2023Membership Inference Attacks against Synthetic Data through Overfitting Detectioncited by 66
  6. 2021Smooth Normalizing Flowscited by 52
  7. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  8. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  9. 2021Tensor-Train Density Estimationcited by 30
  10. 2022Universal approximation property of invertible neural networkscited by 30
  11. 2021Implicit Normalizing Flowscited by 28
  12. 2021Generalized Normalizing Flows via Markov Chainscited by 23
38 more
  1. 2022On minimax density estimation via measure transportcited by 18
  2. 2021Invertible DenseNets with Concatenated LipSwishcited by 17
  3. 2021Autoregressive Quantile Flows for Predictive Uncertainty Estimationcited by 15
  4. 2021Surrogate Likelihoods for Variational Annealed Importance Samplingcited by 14
  5. 2024Data Plagiarism Index: Characterizing the Privacy Risk of Data-Copying in Tabular Generative Modelscited by 12
  6. 2021Density estimation on low-dimensional manifolds: an inflation-deflation approachcited by 11
  7. 2024Privacy Vulnerabilities in Marginals-based Synthetic Datacited by 10
  8. 2024Monotone, Bi-Lipschitz, and Polyak-Lojasiewicz Networkscited by 9
  9. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  10. 2025Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flowscited by 8
  11. 2023Expressive Monotonic Neural Networkscited by 7
  12. 2024Transformer Neural Autoregressive Flowscited by 7
  13. 2024Efficient and Generalized end-to-end Autonomous Driving System with Latent Deep Reinforcement Learning and Demonstrationscited by 7
  14. 2024Importance Corrected Neural JKO Samplingcited by 7
  15. 2024LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transportcited by 7
  16. 2022Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flowscited by 6
  17. 2021Bootstrap Your Flowcited by 5
  18. 2022AUTM Flow: Atomic Unrestricted Time Machine for Monotonic Normalizing Flowscited by 5
  19. 2022Proximal Residual Flows for Bayesian Inverse Problemscited by 5
  20. 2024Local Flow Matching Generative Modelscited by 5
  21. 2025Privacy Auditing Synthetic Data Release through Local Likelihood Attackscited by 5
  22. 2021Marginalizable Density Modelscited by 4
  23. 2022AS-IntroVAE: Adversarial Similarity Distance Makes Robust IntroVAEcited by 4
  24. 2025Efficient Autoregressive Inference for Transformer Probabilistic Modelscited by 4
  25. 2022NFL: Robust Learned Index via Distribution Transformationcited by 3
  26. 2022AdaCat: Adaptive Categorical Discretization for Autoregressive Modelscited by 3
  27. 2022Tackling Multimodal Device Distributions in Inverse Photonic Design using Invertible Neural Networkscited by 3
  28. 2022Normalizing Flows for Hierarchical Bayesian Analysis: A Gravitational Wave Population Studycited by 3
  29. 2024Variational Inference of Parameters in Opinion Dynamics Modelscited by 3
  30. 2021Visual Attention in Imaginative Agentscited by 2
  31. 2022Neural Inverse Transform Samplercited by 2
  32. 2023On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networkscited by 2
  33. 2023Reparameterized Variational Rejection Samplingcited by 2
  34. 2023TERM Model: Tensor Ring Mixture Model for Density Estimationcited by 2
  35. 2025Accelerate TarFlow Sampling with GS-Jacobi Iterationcited by 2
  36. 2021Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regressioncited by 1
  37. 2021ELF: Exact-Lipschitz Based Universal Density Approximator Flowcited by 1
  38. 2024Mixed Noise and Posterior Estimation with Conditional DeepGEMcited by 1

50 most cited of 62 All 62 (JSON)