# Wrapped Distributions on homogeneous Riemannian manifolds

arXiv: https://arxiv.org/abs/2204.09790 · HTML: https://mlsanity.com/paper/2204.09790/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 20 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [Adversarial Autoencoders with Constant-Curvature Latent Manifolds](https://mlsanity.com/paper/1812.04314/) (2018)
- [The Geometry of Continuous Latent Space Models for Network Data](https://mlsanity.com/paper/1712.08641/) (2017)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [Poincar'e Wasserstein Autoencoder](https://mlsanity.com/paper/1901.01427/) (2019)
- [A Wrapped Normal Distribution on Hyperbolic Space for Gradient-Based Learning](https://mlsanity.com/paper/1902.02992/) (2019)
- [Fast generation of complex networks with underlying hyperbolic geometry](https://mlsanity.com/paper/1501.03545/) (2015)
- [How to see the eight Thurston geometries](https://mlsanity.com/paper/2005.12772/) (2020)

## Built on by (most cited first, 9 of 9)

- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Fast and Robust Visuomotor Riemannian Flow Matching Policy](https://mlsanity.com/paper/2412.10855/) (2024)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [Gaussian Differential Privacy on Riemannian Manifolds](https://mlsanity.com/paper/2311.10101/) (2023)
- [Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2502.01512/) (2025)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [Changes from Classical Statistics to Modern Statistics and Data Science](https://mlsanity.com/paper/2211.03756/) (2022)
- [Radial Compensation: The Inverse Base-Distribution Problem for Chart-Based Generative Models on Riemannian Manifolds](https://mlsanity.com/paper/2511.14056/) (2025)

## Abstract (arXiv)

We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions that are straightforward to sample from, suitable for use within Monte Carlo algorithms and latent variable models, such as autoencoders. As an illustration, we empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model. Finally, we take advantage of the generalized description of this framework to posit questions for future work.