mlsanityData to 7 Oct 2026

Neural Spline Flows

arXiv 1906.04032 ↗First posted 10 Jun 2019stat.ML cs.LGcited by 590

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Cited by 34 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

Key facts. Cited by 590 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 75; 2022: 83; 2023: 120; 2024: 91; 2025: 116; 2026: 105.

590 papers.

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  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  4. 2022Continuous diffusion for categorical datacited by 202
  5. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  6. 2021Benchmarking Simulation-Based Inferencecited by 160
  7. 2022Liquid Structural State-Space Modelscited by 134
  8. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  9. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  10. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 97
  11. 2023Stochastic interpolants with data-dependent couplingscited by 94
  12. 2022Deep End-to-end Causal Inferencecited by 93
38 more
  1. 2021Annealed Flow Transport Monte Carlocited by 90
  2. 2021Real-time gravitational-wave science with neural posterior estimationcited by 76
  3. 2023Membership Inference Attacks against Synthetic Data through Overfitting Detectioncited by 66
  4. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  5. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  6. 2021Density Ratio Estimation via Infinitesimal Classificationcited by 59
  7. 2022From Denoising Diffusions to Denoising Markov Modelscited by 58
  8. 2023normflows: A PyTorch Package for Normalizing Flowscited by 56
  9. 2023Causal Component Analysiscited by 56
  10. 2021Recent Advances of Continual Learning in Computer Vision: An Overviewcited by 55
  11. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  12. 2021Smooth Normalizing Flowscited by 52
  13. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  14. 2021Rectangular Flows for Manifold Learningcited by 49
  15. 2023Causal normalizing flows: from theory to practicecited by 49
  16. 2021CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flowscited by 46
  17. 2021Learning Disentangled Representations in the Imaging Domaincited by 46
  18. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  19. 2022Investigating the Impact of Model Misspecification in Neural Simulation-based Inferencecited by 44
  20. 2022Variational methods for simulation-based inferencecited by 43
  21. 2021Resampling Base Distributions of Normalizing Flowscited by 42
  22. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  23. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  24. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Modelscited by 41
  25. 2022Truncated proposals for scalable and hassle-free simulation-based inferencecited by 40
  26. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
  27. 2021Fair Normalizing Flowscited by 38
  28. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  29. 2021Trumpets: Injective Flows for Inference and Inverse Problemscited by 36
  30. 2022Flow-matching -- efficient coarse-graining of molecular dynamics without forcescited by 36
  31. 2021Copula Flows for Synthetic Data Generationcited by 35
  32. 2021CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flowscited by 34
  33. 2023CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulationcited by 33
  34. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  35. 2021Sequential Neural Posterior and Likelihood Approximationcited by 30
  36. 2021Mean Field Games Flock! The Reinforcement Learning Waycited by 30
  37. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 30
  38. 2022LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihoodcited by 30

50 most cited of 590 All 590 (JSON)