# (Deep) Generative Geodesics

arXiv: https://arxiv.org/abs/2407.11244 · HTML: https://mlsanity.com/paper/2407.11244/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Understanding and Improving Interpolation in Autoencoders via an Adversarial Regularizer](https://mlsanity.com/paper/1807.07543/) (2018)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Metrics for Deep Generative Models](https://mlsanity.com/paper/1711.01204/) (2017)
- [Low-Rank Subspaces in GANs](https://mlsanity.com/paper/2106.04488/) (2021)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [A Spectral Regularizer for Unsupervised Disentanglement](https://mlsanity.com/paper/1812.01161/) (2018)
- [Do Not Escape From the Manifold: Discovering the Local Coordinates on the Latent Space of GANs](https://mlsanity.com/paper/2106.06959/) (2021)
- [Learning Disentangled Representations with Latent Variation Predictability](https://mlsanity.com/paper/2007.12885/) (2020)
- [Latent Traversals in Generative Models as Potential Flows](https://mlsanity.com/paper/2304.12944/) (2023)
- [On Explicit Curvature Regularization in Deep Generative Models](https://mlsanity.com/paper/2309.10237/) (2023)
- [A prior-based approximate latent Riemannian metric](https://mlsanity.com/paper/2103.05290/) (2021)
- [On Linear Interpolation in the Latent Space of Deep Generative Models](https://mlsanity.com/paper/2105.03663/) (2021)
- [Approximating geodesics via random points](https://mlsanity.com/paper/1711.06952/) (2017)
- [Feature-Based Interpolation and Geodesics in the Latent Spaces of Generative Models](https://mlsanity.com/paper/1904.03445/) (2019)
- [Unveiling the Latent Space Geometry of Push-Forward Generative Models](https://mlsanity.com/paper/2207.10541/) (2022)

## Built on by (most cited first, 1 of 1)

- [PepCompass: Navigating peptide embedding spaces using Riemannian Geometry](https://mlsanity.com/paper/2510.01988/) (2025)

## Abstract (arXiv)

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization of the generative model and requires only the evaluation of its data likelihood. Moreover, the metric leads to the conceptual definition of generative distances and generative geodesics, whose computation can be done efficiently in the data space. Their approximations are proven to converge to their true values under mild conditions. We showcase three proof-of-concept applications of this global metric, including clustering, data visualization, and data interpolation, thus providing new tools to support the geometrical understanding of generative models.