mlsanityData to 7 Oct 2026

Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

arXiv 2203.03934 ↗First posted 8 Mar 2022cs.LGcited by 5

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Abstract (arXiv)

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 8 Mar 2022.

Builds on

22 of 45 references.

References · 22

  1. 2022Generative Adversarial Networkscited by 5,603
  2. 2016Improved Techniques for Training GANscited by 2,938
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
  8. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  9. 2020Normalizing Flows on Tori and Spherescited by 117
  10. 2020Flows for simultaneous manifold learning and density estimationcited by 117
  11. 2020Neural Manifold Ordinary Differential Equationscited by 81
  12. 2020Understanding and Mitigating Exploding Inverses in Invertible Neural Networkscited by 71
10 more
  1. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  2. 2021Rectangular Flows for Manifold Learningcited by 49
  3. 2021Trumpets: Injective Flows for Inference and Inverse Problemscited by 36
  4. 2020LOCA: LOcal Conformal Autoencoder for standardized data coordinatescited by 19
  5. 2020Normalizing Flows Across Dimensionscited by 19
  6. 2020Isometric Autoencoderscited by 18
  7. 2013Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discoverycited by 14
  8. 2021Density estimation on low-dimensional manifolds: an inflation-deflation approachcited by 11
  9. 2021Principal Component Density Estimation for Scenario Generation Using Normalizing Flowscited by 10
  10. 2022Principal Manifold Flowscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 1; 2025: 0; 2026: 1.

5 papers.

  1. 2023Lifting Architectural Constraints of Injective Flowscited by 17
  2. 2023Canonical normalizing flows for manifold learningcited by 15
  3. 2022Deterministic training of generative autoencoders using invertible layerscited by 3
  4. 2024Analyzing Generative Models by Manifold Entropic Metricscited by 2
  5. 2026FloDR: An invertible dimensionality reduction method based on a normalising flowcited by 0