# Geodesic Clustering in Deep Generative Models

arXiv: https://arxiv.org/abs/1809.04747 · HTML: https://mlsanity.com/paper/1809.04747/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2018.

## Built on by (most cited first, 14 of 14)

- [Pulling back information geometry](https://mlsanity.com/paper/2106.05367/) (2021)
- [A prior-based approximate latent Riemannian metric](https://mlsanity.com/paper/2103.05290/) (2021)
- [Exploring the Latent Space of Autoencoders with Interventional Assays](https://mlsanity.com/paper/2106.16091/) (2021)
- [On Linear Interpolation in the Latent Space of Deep Generative Models](https://mlsanity.com/paper/2105.03663/) (2021)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Decoder ensembling for learned latent geometries](https://mlsanity.com/paper/2408.07507/) (2024)
- [Adversarial robustness of VAEs through the lens of local geometry](https://mlsanity.com/paper/2208.03923/) (2022)
- [Using the Path of Least Resistance to Explain Deep Networks](https://mlsanity.com/paper/2502.12108/) (2025)
- [Connecting Neural Models Latent Geometries with Relative Geodesic Representations](https://mlsanity.com/paper/2506.01599/) (2025)
- [Learning Geometry and Topology via Multi-Chart Flows](https://mlsanity.com/paper/2505.24665/) (2025)
- [Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models](https://mlsanity.com/paper/2510.05509/) (2025)
- [Training Deep Normalizing Flow Models in Highly Incomplete Data Scenarios with Prior Regularization](https://mlsanity.com/paper/2104.01482/) (2021)
- [Discriminating Against Unrealistic Interpolations in Generative Adversarial Networks](https://mlsanity.com/paper/2203.01035/) (2022)
- [Geometric Embedding Alignment via Curvature Matching in Transfer Learning](https://mlsanity.com/paper/2506.13015/) (2025)

## Abstract (arXiv)

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances tend to not reflect semantic similarities well. This renders unsupervised tasks, such as clustering, difficult when working with the latent representations. We demonstrate that taking the geometry of the generative model into account is sufficient to make simple clustering algorithms work well over latent representations. Leaning on the recent finding that deep generative models constitute stochastically immersed Riemannian manifolds, we propose an efficient algorithm for computing geodesics (shortest paths) and computing distances in the latent space, while taking its distortion into account. We further propose a new architecture for modeling uncertainty in variational autoencoders, which is essential for understanding the geometry of deep generative models. Experiments show that the geodesic distance is very likely to reflect the internal structure of the data.