mlsanityData to 7 Oct 2026

VQ-Flows: Vector Quantized Local Normalizing Flows

arXiv 2203.11556 ↗First posted 22 Mar 2022cs.LG cs.AI stat.MLcited by 10

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Abstract (arXiv)

Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a low-dimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized auto-encoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 33 of its 44 references that are in the map. First posted on arXiv 22 Mar 2022.

Builds on

33 of 44 references.

References · 33

  1. 2017Neural Discrete Representation Learningcited by 4,650
  2. 2013Auto-Encoding Variational Bayescited by 3,980
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2016Density estimation using Real NVPcited by 2,029
  6. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  7. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  8. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  9. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  10. 2019Neural Spline Flowscited by 590
  11. 2019Augmented Neural ODEscited by 396
  12. 2018Invertible Residual Networkscited by 364
21 more
  1. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  2. 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
  3. 2022AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generationcited by 208
  4. 2018Neural Autoregressive Flowscited by 207
  5. 2019Diagnosing and Enhancing VAE Modelscited by 192
  6. 2020Riemannian Continuous Normalizing Flowscited by 143
  7. 2015Density Modeling of Images using a Generalized Normalization Transformationcited by 123
  8. 2020Flows for simultaneous manifold learning and density estimationcited by 117
  9. 2020Understanding and Mitigating Exploding Inverses in Invertible Neural Networkscited by 71
  10. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  11. 2019Sum-of-Squares Polynomial Flowcited by 62
  12. 2021Rectangular Flows for Manifold Learningcited by 49
  13. 2020Composing Normalizing Flows for Inverse Problemscited by 48
  14. 2019Structured Output Learning with Conditional Generative Flowscited by 37
  15. 2021Trumpets: Injective Flows for Inference and Inverse Problemscited by 36
  16. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 30
  17. 2018Disconnected Manifold Learning for Generative Adversarial Networkscited by 27
  18. 2020Bi-Directional Generation for Unsupervised Domain Adaptationcited by 26
  19. 2020Regularized Autoencoders via Relaxed Injective Probability Flowcited by 23
  20. 2020Normalizing Flows Across Dimensionscited by 19
  21. 2019A RAD approach to deep mixture modelscited by 18

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 3; 2025: 2; 2026: 2.

10 papers.

  1. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  2. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  3. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 12
  4. 2022Neural Implicit Manifold Learning for Topology-Aware Density Estimationcited by 5
  5. 2024A Unified Framework for Human-Allied Learning of Probabilistic Circuitscited by 5
  6. 2024ContextFlow++: Generalist-Specialist Flow-based Generative Models with Mixed-Variable Context Encodingcited by 3
  7. 2025Learning Geometry and Topology via Multi-Chart Flowscited by 3
  8. 2026Geometry-Aware Probabilistic Circuits via Voronoi Tessellationscited by 1
  9. 2025Normalizing Flows on Quotient Manifolds via Boundary Quotientscited by 0
  10. 2026Field Codes for Distributed Coupling Samplers and Certified Empirical Transportcited by 0