mlsanityData to 7 Oct 2026

Resampling Base Distributions of Normalizing Flows

arXiv 2110.15828 ↗First posted 29 Oct 2021stat.ML cs.AI cs.LGcited by 42

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Abstract (arXiv)

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). Builds on 37 of its 54 references that are in the map. First posted on arXiv 29 Oct 2021.

Builds on

37 of 54 references.

References · 37

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
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  6. 2017Improved Training of Wasserstein GANscited by 2,223
  7. 2015Variational Inference with Normalizing Flowscited by 2,161
  8. 2016Density estimation using Real NVPcited by 2,029
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25 more
  1. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  2. 2021Variational Diffusion Modelscited by 1,145
  3. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  4. 2018Image Transformercited by 770
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  6. 2019Neural Spline Flowscited by 590
  7. 2018Invertible Residual Networkscited by 364
  8. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  9. 2019Residual Flows for Invertible Generative Modelingcited by 256
  10. 2017The Reversible Residual Network: Backpropagation Without Storing Activationscited by 215
  11. 2017Parallel WaveNet: Fast High-Fidelity Speech Synthesiscited by 214
  12. 2020Stochastic Normalizing Flowscited by 156
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  14. 2019Semi-Supervised Learning with Normalizing Flowscited by 76
  15. 2020Understanding and Mitigating Exploding Inverses in Invertible Neural Networkscited by 71
  16. 2020SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flowscited by 71
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  18. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  19. 2018Resampled Priors for Variational Autoencoderscited by 56
  20. 2021Smooth Normalizing Flowscited by 52
  21. 2021Densely connected normalizing flowscited by 49
  22. 2019MaCow: Masked Convolutional Generative Flowcited by 32
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  24. 2018Variational Rejection Samplingcited by 13
  25. 2020Normalizing Flows with Multi-Scale Autoregressive Priorscited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 16; 2024: 5; 2025: 13; 2026: 5.

42 papers.

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  1. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  2. 2023Improved sampling via learned diffusionscited by 103
  3. 2023normflows: A PyTorch Package for Normalizing Flowscited by 56
  4. 2025On the Guidance of Flow Matchingcited by 44
  5. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  6. 2024On the Challenges and Opportunities in Generative AIcited by 31
  7. 2024Diffusive Gibbs Samplingcited by 21
  8. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  9. 2023Squared Neural Families: A New Class of Tractable Density Modelscited by 12
  10. 2023Designing losses for data-free training of normalizing flows on Boltzmann distributionscited by 9
  11. 2023Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flowscited by 9
  12. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
30 more
  1. 2023Training, Architecture, and Prior for Deterministic Uncertainty Methodscited by 7
  2. 2023Normalizing flow sampling with Langevin dynamics in the latent spacecited by 7
  3. 2023Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learningcited by 7
  4. 2024AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learningcited by 6
  5. 2021Bootstrap Your Flowcited by 5
  6. 2023Optimal Budgeted Rejection Sampling for Generative Modelscited by 5
  7. 2026Action Hallucination in Generative Vision-Language-Action Modelscited by 5
  8. 2023Learning Distributions via Monte-Carlo Marginalizationcited by 4
  9. 2025Evaluating multiple models using labeled and unlabeled datacited by 4
  10. 2025Learning Geometry and Topology via Multi-Chart Flowscited by 3
  11. 2022Nonlinear MCMC for Bayesian Machine Learningcited by 2
  12. 2023Density-based Feasibility Learning with Normalizing Flows for Introspective Robotic Assemblycited by 2
  13. 2023Reparameterized Variational Rejection Samplingcited by 2
  14. 2025Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Datacited by 2
  15. 2025Generative Machine Learning for Multivariate Angular Simulationcited by 2
  16. 2025Wavelet Flow For Extragalactic Foreground Simulationscited by 2
  17. 2026Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularizationcited by 2
  18. 2023Piecewise Normalizing Flowscited by 1
  19. 2023Variations and Relaxations of Normalizing Flowscited by 1
  20. 2024Accelerated Bayesian parameter estimation and model selection for gravitational waves with normalizing flowscited by 1
  21. 2025Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluationscited by 1
  22. 2023Training Normalizing Flows with the Precision-Recall Divergencecited by 0
  23. 2024Controlling for discrete unmeasured confounding in nonlinear causal modelscited by 0
  24. 2025Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesiscited by 0
  25. 2025Adaptive Heterogeneous Mixtures of Normalising Flows for Robust Variational Inferencecited by 0
  26. 2025Score-Based Density Estimation from Pairwise Comparisonscited by 0
  27. 2025Adapting Noise to Data: Generative Flows from 1D Processescited by 0
  28. 2026Correcting Source Mismatch in Flow Matching with Radial-Angular Transportcited by 0
  29. 2026Implicit Variational Rejection Samplingcited by 0
  30. 2026Simplifying Flow Matching Transformations with Low-Rank Mixture Modelscited by 0