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Flows for simultaneous manifold learning and density estimation

arXiv 2003.13913 ↗First posted 31 Mar 2020stat.ML cs.LGcited by 117

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Abstract (arXiv)

We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent datasets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. In a range of experiments we demonstrate how M-flows learn the data manifold and allow for better inference than standard flows in the ambient data space.

Key facts. Cited by 117 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Mar 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 23; 2022: 30; 2023: 28; 2024: 15; 2025: 14; 2026: 7.

117 papers.

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  1. 2022Riemannian Score-Based Generative Modellingcited by 216
  2. 2022Weakly supervised causal representation learningcited by 140
  3. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  4. 2022Riemannian Diffusion Modelscited by 120
  5. 2021A Living Review of Machine Learning for Particle Physicscited by 77
  6. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  7. 2021Smooth Normalizing Flowscited by 52
  8. 2021Rectangular Flows for Manifold Learningcited by 49
  9. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  10. 2021CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flowscited by 46
  11. 2021Trumpets: Injective Flows for Inference and Inverse Problemscited by 36
  12. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 30
38 more
  1. 2022LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihoodcited by 30
  2. 2023Explicitly Minimizing the Blur Error of Variational Autoencoderscited by 29
  3. 2022Diagnosing and Fixing Manifold Overfitting in Deep Generative Modelscited by 28
  4. 2021Autoencoding Under Normalization Constraintscited by 26
  5. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  6. 2024Mutual Information Estimation via Normalizing Flowscited by 22
  7. 2024A Geometric Explanation of the Likelihood OOD Detection Paradoxcited by 22
  8. 2024Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groupscited by 19
  9. 2023Scaling Riemannian Diffusion Modelscited by 18
  10. 2023Deep Generative Models for Detector Signature Simulation: A Taxonomic Reviewcited by 18
  11. 2021Understanding Event-Generation Networks via Uncertaintiescited by 17
  12. 2023Lifting Architectural Constraints of Injective Flowscited by 17
  13. 2021Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstructioncited by 16
  14. 2021Riemannian Convex Potential Mapscited by 16
  15. 2021Entropic Issues in Likelihood-Based OOD Detectioncited by 16
  16. 2021E Pluribus Unum Ex Machina: Learning from Many Collider Events at Oncecited by 15
  17. 2023Canonical normalizing flows for manifold learningcited by 15
  18. 2022Adaptive and Dynamic Multi-Resolution Hashing for Pairwise Summationscited by 14
  19. 2023Self-supervised Representation Learning From Random Data Projectorscited by 14
  20. 2024Neural Contractive Dynamical Systemscited by 14
  21. 2021Universal Joint Approximation of Manifolds and Densities by Simple Injective Flowscited by 13
  22. 2022Conditional Injective Flows for Bayesian Imagingcited by 13
  23. 2023On Explicit Curvature Regularization in Deep Generative Modelscited by 13
  24. 2022Effects of Data Geometry in Early Deep Learningcited by 12
  25. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 12
  26. 2021Density estimation on low-dimensional manifolds: an inflation-deflation approachcited by 11
  27. 2022TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantificationcited by 11
  28. 2022Gradual Domain Adaptation via Normalizing Flowscited by 11
  29. 2022nu-Flows: Conditional Neutrino Regressioncited by 11
  30. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  31. 2025Accurate Forgetting for Heterogeneous Federated Continual Learningcited by 11
  32. 2021Principal Component Density Estimation for Scenario Generation Using Normalizing Flowscited by 10
  33. 2021Latent Space Refinement for Deep Generative Modelscited by 10
  34. 2021Density estimation on smooth manifolds with normalizing flowscited by 10
  35. 2021Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distancecited by 10
  36. 2022VQ-Flows: Vector Quantized Local Normalizing Flowscited by 10
  37. 2023Injectivity of ReLU networks: perspectives from statistical physicscited by 10
  38. 2024Distributional Principal Autoencoderscited by 10

50 most cited of 117 All 117 (JSON)