mlsanityData to 7 Oct 2026

A prior-based approximate latent Riemannian metric

arXiv 2103.05290 ↗First posted 9 Mar 2021stat.ML cs.LGcited by 11

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Abstract (arXiv)

Stochastic generative models enable us to capture the geometric structure of a data manifold lying in a high dimensional space through a Riemannian metric in the latent space. However, its practical use is rather limited mainly due to inevitable complexity. In this work we propose a surrogate conformal Riemannian metric in the latent space of a generative model that is simple, efficient and robust. This metric is based on a learnable prior that we propose to learn using a basic energy-based model. We theoretically analyze the behavior of the proposed metric and show that it is sensible to use in practice. We demonstrate experimentally the efficiency and robustness, as well as the behavior of the new approximate metric. Also, we show the applicability of the proposed methodology for data analysis in the life sciences.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 21 of its 40 references that are in the map. First posted on arXiv 9 Mar 2021.

Builds on

21 of 40 references.

References · 21

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9 more
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Built on by

Cited by year

Citing papers per year: 2021: 2; 2022: 0; 2023: 2; 2024: 3; 2025: 4.

11 papers.

  1. 2023Norm-guided latent space exploration for text-to-image generationcited by 43
  2. 2021Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencodercited by 27
  3. 2024Pulling back symmetric Riemannian geometry for data analysiscited by 8
  4. 2023RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representationscited by 7
  5. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  6. 2021Learning Identity-Preserving Transformations on Data Manifoldscited by 4
  7. 2025Image Interpolation with Score-based Riemannian Metrics of Diffusion Modelscited by 4
  8. 2025Connecting Neural Models Latent Geometries with Relative Geodesic Representationscited by 4
  9. 2024(Deep) Generative Geodesicscited by 1
  10. 2025Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Modelscited by 1
  11. 2024Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimationcited by 0