mlsanityData to 7 Oct 2026

Geometrically Enriched Latent Spaces

arXiv 2008.00565 ↗First posted 2 Aug 2020stat.ML cs.LGcited by 45

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Abstract (arXiv)

A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Aug 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 7; 2023: 5; 2024: 10; 2025: 10; 2026: 5.

45 papers.

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  1. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometrycited by 121
  2. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  3. 2023Unsupervised Discovery of Semantic Latent Directions in Diffusion Modelscited by 28
  4. 2021Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencodercited by 27
  5. 2021Learning Riemannian Manifolds for Geodesic Motion Skillscited by 23
  6. 2021Pulling back information geometrycited by 23
  7. 2022Attribution-based Explanations that Provide Recourse Cannot be Robustcited by 20
  8. 2021A prior-based approximate latent Riemannian metriccited by 11
  9. 2021Uncertainty Estimation Using Riemannian Model Dynamics for Offline Reinforcement Learningcited by 10
  10. 2021GeomCA: Geometric Evaluation of Data Representationscited by 9
  11. 2024Embedding-Aligned Language Modelscited by 9
  12. 2024Counterfactual Explanations via Riemannian Latent Space Traversalcited by 9
33 more
  1. 2026The Information Geometry of Softmax: Probing and Steeringcited by 9
  2. 2024Pulling back symmetric Riemannian geometry for data analysiscited by 8
  3. 2024Pullback Flow Matching on Data Manifoldscited by 8
  4. 2023A Geometric Perspective on Autoencoderscited by 7
  5. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  6. 2022Reactive Motion Generation on Learned Riemannian Manifoldscited by 6
  7. 2023Unsupervised Discovery of Interpretable Directions in h-space of Pre-trained Diffusion Modelscited by 6
  8. 2024Decoder ensembling for learned latent geometriescited by 6
  9. 2021Bayesian Quadrature on Riemannian Data Manifoldscited by 5
  10. 2025Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolationcited by 5
  11. 2022Adversarial robustness of VAEs through the lens of local geometrycited by 4
  12. 2024Generalized Flow Matching for Transition Dynamics Modelingcited by 4
  13. 2025Image Interpolation with Score-based Riemannian Metrics of Diffusion Modelscited by 4
  14. 2025Connecting Neural Models Latent Geometries with Relative Geodesic Representationscited by 4
  15. 2022Deep Curvilinear Editing: Commutative and Nonlinear Image Manipulation for Pretrained Deep Generative Modelcited by 3
  16. 2021Geometry and Generalization: Eigenvalues as predictors of where a network will fail to generalizecited by 2
  17. 2025Geodesic Calculus on Implicitly Defined Latent Manifoldscited by 2
  18. 2025Latent Diffusion Inversion Requires Understanding the Latent Spacecited by 2
  19. 2022Geometric instability of out of distribution data across autoencoder architecturecited by 1
  20. 2022Active Nearest Neighbor Regression Through Delaunay Refinementcited by 1
  21. 2024(Deep) Generative Geodesicscited by 1
  22. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  23. 2025Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Modelscited by 1
  24. 2026Riemannian Metric Matching for Scalable Geometric Modeling of Distributionscited by 1
  25. 2022Discriminating Against Unrealistic Interpolations in Generative Adversarial Networkscited by 0
  26. 2023Short and Straight: Geodesics on Differentiable Manifoldscited by 0
  27. 2024A Metric-based Principal Curve Approach for Learning One-dimensional Manifoldcited by 0
  28. 2025Energy Guided Geometric Flow Matchingcited by 0
  29. 2025PepCompass: Navigating peptide embedding spaces using Riemannian Geometrycited by 0
  30. 2025The Neural Differential Manifold: An Architecture with Explicit Geometric Structurecited by 0
  31. 2026Learning a Latent Pulse Shape Interface for Photoinjector Laser Systemscited by 0
  32. 2026Deep Image Prototype Learning with Geometric Heat-Kernel Priorscited by 0
  33. 2026Stable Autoregressive Speech Generation with Low-Frame-Rate High-Dimensional Continuous Tokenscited by 0