mlsanityData to 7 Oct 2026

Free-form Flows: Make Any Architecture a Normalizing Flow

arXiv 2310.16624 ↗First posted 25 Oct 2023cs.LG stat.MLcited by 26

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Abstract (arXiv)

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure that uses an efficient estimator for the gradient of the change of variables formula. This enables any dimension-preserving neural network to serve as a generative model through maximum likelihood training. Our approach allows placing the emphasis on tailoring inductive biases precisely to the task at hand. Specifically, we achieve excellent results in molecule generation benchmarks utilizing E(n)-equivariant networks. Moreover, our method is competitive in an inverse problem benchmark, while employing off-the-shelf ResNet architectures.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 40 of its 70 references that are in the map. First posted on arXiv 25 Oct 2023.

Builds on

40 of 70 references.

References · 40

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2022Flow Matching for Generative Modelingcited by 5,426
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2016Density estimation using Real NVPcited by 2,029
  8. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  9. 2018On the Spectral Bias of Neural Networkscited by 1,321
  10. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  11. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  12. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
28 more
  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  3. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  4. 2019Neural Spline Flowscited by 590
  5. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  6. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  7. 2018Invertible Residual Networkscited by 364
  8. 2016Revisiting Classifier Two-Sample Testscited by 258
  9. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  10. 2019Residual Flows for Invertible Generative Modelingcited by 256
  11. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  12. 2021E(n) Equivariant Normalizing Flowscited by 165
  13. 2021Benchmarking Simulation-Based Inferencecited by 160
  14. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  15. 2019Hamiltonian Generative Networkscited by 136
  16. 2023Equivariant flow matchingcited by 131
  17. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 97
  18. 2020Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximatorscited by 85
  19. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  20. 2021Rectangular Flows for Manifold Learningcited by 49
  21. 2020Representational aspects of depth and conditioning in normalizing flowscited by 25
  22. 2018Spread Divergencecited by 23
  23. 2020OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germanycited by 17
  24. 2023Lifting Architectural Constraints of Injective Flowscited by 17
  25. 2020Relative gradient optimization of the Jacobian term in unsupervised deep learningcited by 16
  26. 2020Self Normalizing Flowscited by 12
  27. 2022Whitening Convergence Rate of Coupling-based Normalizing Flowscited by 6
  28. 2023On the Convergence Rate of Gaussianization with Random Rotationscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 13; 2026: 8.

26 papers.

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  1. 2024Transferable Boltzmann Generatorscited by 43
  2. 2025FARMER: Flow AutoRegressive Transformer over Pixelscited by 17
  3. 2025FALCON: Few-step Accurate Likelihoods for Continuous Flowscited by 12
  4. 2023Learning Distributions on Manifolds with Free-Form Flowscited by 7
  5. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  6. 2026BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Pythoncited by 7
  7. 2025SimFlow: Simplified and End-to-End Training of Latent Normalizing Flowscited by 6
  8. 2025Parallel Token Prediction for Language Modelscited by 6
  9. 2024Conditional Normalizing Flows for Active Learning of Coarse-Grained Molecular Representationscited by 5
  10. 2025Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometrycited by 5
  11. 2025Tractable Representation Learning with Probabilistic Circuitscited by 4
  12. 2026Calibrated Test-Time Guidance for Bayesian Inferencecited by 4
14 more
  1. 2024TRADE: Transfer of Distributions between External Conditions with Normalizing Flowscited by 3
  2. 2025Learning Geometry and Topology via Multi-Chart Flowscited by 3
  3. 2024Analyzing Generative Models by Manifold Entropic Metricscited by 2
  4. 2025Path Gradients after Flow Matchingcited by 2
  5. 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Mapscited by 2
  6. 2025Beyond Diagonal Covariance: Flexible Posterior VAEs via Free-Form Injective Flowscited by 1
  7. 2026Analytic Bijections for Smooth and Interpretable Normalizing Flowscited by 1
  8. 2026MIMFlow: Integrating Masked Image Modeling with Normalizing Flows for End-to-End Image Generationcited by 1
  9. 2026Autoregressive Boltzmann Generatorscited by 1
  10. 2025Operator Forces For Coarse-Grained Molecular Dynamicscited by 0
  11. 2025Marginal Flow: a flexible and efficient framework for density estimationcited by 0
  12. 2025Matricial Free Energy as a Gaussianizing Regularizer: Enhancing Autoencoders for Gaussian Code Generationcited by 0
  13. 2026Show Me What You Don't Know: Efficient Sampling from Invariant Sets for Model Validationcited by 0
  14. 2026Likelihood-free inference with nuisance parameters through normalizing flowscited by 0