mlsanityData to 7 Oct 2026

A Geometric Perspective on Variational Autoencoders

arXiv 2209.07370 ↗First posted 15 Sep 2022stat.ML cs.LGcited by 24

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Abstract (arXiv)

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 36 of its 73 references that are in the map. First posted on arXiv 15 Sep 2022.

Builds on

36 of 73 references.

References · 36

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2015Variational Inference with Normalizing Flowscited by 2,161
  4. 2019Generating Diverse High-Fidelity Images with VQ-VAE-2cited by 1,376
  5. 2016Deep Variational Information Bottleneckcited by 915
  6. 2016InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Netscited by 858
  7. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  8. 2015Importance Weighted Autoencoderscited by 454
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  10. 2018Assessing Generative Models via Precision and Recallcited by 401
  11. 2017Wasserstein Auto-Encoderscited by 371
  12. 2015Adversarial Autoencoderscited by 359
24 more
  1. 2017VAE with a VampPriorcited by 247
  2. 2017Advances in Variational Inferencecited by 236
  3. 2016Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoderscited by 219
  4. 2019Diagnosing and Enhancing VAE Modelscited by 192
  5. 2018Hyperspherical Variational Auto-Encoderscited by 188
  6. 2016Variational Lossy Autoencodercited by 175
  7. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 169
  8. 2018Inference Suboptimality in Variational Autoencoderscited by 131
  9. 2019From Variational to Deterministic Autoencoderscited by 131
  10. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  11. 2020Learning Latent Space Energy-Based Prior Modelcited by 104
  12. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 103
  13. 2018Variational Autoencoders Pursue PCA Directions (by Accident)cited by 84
  14. 2017The Riemannian Geometry of Deep Generative Modelscited by 81
  15. 2018Explorations in Homeomorphic Variational Auto-Encodingcited by 65
  16. 2018Resampled Priors for Variational Autoencoderscited by 56
  17. 2017Metrics for Deep Generative Modelscited by 53
  18. 2019Learning Hierarchical Priors in VAEscited by 53
  19. 2018Hamiltonian Variational Auto-Encodercited by 41
  20. 2020Variational Autoencoder with Learned Latent Structurecited by 41
  21. 2020On Implicit Regularization in β-VAEscited by 34
  22. 2020Variational Autoencoders with Riemannian Brownian Motion Priorscited by 34
  23. 2021Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencodercited by 27
  24. 2020Geometry-Aware Hamiltonian Variational Auto-Encodercited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 8; 2025: 6; 2026: 5.

24 papers.

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  1. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  2. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  3. 2023VTAE: Variational Transformer Autoencoder with Manifolds Learningcited by 10
  4. 2024The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanationscited by 5
  5. 2025Connecting Neural Models Latent Geometries with Relative Geodesic Representationscited by 4
  6. 2024Ricci flow regularization in latent spaces for the forward learning of partial differential equationscited by 2
  7. 2024Latent Space Characterization of Autoencoder Variantscited by 2
  8. 2025Latent Diffusion Inversion Requires Understanding the Latent Spacecited by 2
  9. 2024A mathematical framework of intelligence and consciousness based on Riemannian Geometrycited by 1
  10. 2023Variational Inference for Longitudinal Data Using Normalizing Flowscited by 0
  11. 2023Learning Pose Image Manifolds Using Geometry-Preserving GANs and Elasticaecited by 0
  12. 2023Illumination and Shadows in Head Rotation: experiments with Denoising Diffusion Modelscited by 0
12 more
  1. 2023Sampling From Autoencoders' Latent Space via Quantization And Probability Mass Function Conceptscited by 0
  2. 2024Variational autoencoders with latent high-dimensional steady geometric flows for dynamicscited by 0
  3. 2024Disentanglement as Identifiable Pushforward Factorisationcited by 0
  4. 2025Assessing local deformation and computing scalar curvature with nonlinear conformal regularization of decoderscited by 0
  5. 2025Privacy-Utility Trade-off in Data Publication: A Bilevel Optimization Framework with Curvature-Guided Perturbationcited by 0
  6. 2025A Geometric Unification of Generative AI with Manifold-Probabilistic Projection Modelscited by 0
  7. 2025Complex variational autoencoders admit K"ahler structurecited by 0
  8. 2026Local EGOP for Continuous Index Learningcited by 0
  9. 2026Hyperparameter Trajectory Inference with Conditional Lagrangian Optimal Transportcited by 0
  10. 2026Manifold-Matching Autoencoderscited by 0
  11. 2026Geometric Decoupling: Diagnosing the Structural Instability of Latentcited by 0
  12. 2026An Elastic Shape Variational Autoencoder for Skeleton Pose Trajectoriescited by 0