# Diffeomorphic density matching by optimal information transport

arXiv: https://arxiv.org/abs/1501.07635 · HTML: https://mlsanity.com/paper/1501.07635/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2015.

## Built on by (most cited first, 7 of 7)

- [Federated Wasserstein Distance](https://mlsanity.com/paper/2310.01973/) (2023)
- [Diffeomorphic Measure Matching with Kernels for Generative Modeling](https://mlsanity.com/paper/2402.08077/) (2024)
- [Structural Connectome Atlas Construction in the Space of Riemannian Metrics](https://mlsanity.com/paper/2103.05730/) (2021)
- [Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics](https://mlsanity.com/paper/2109.09808/) (2021)
- [A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints](https://mlsanity.com/paper/2308.02393/) (2023)
- [A Relaxed Wasserstein Distance Formulation for Mixtures of Radially Contoured Distributions](https://mlsanity.com/paper/2503.13893/) (2025)
- [Coupled Optimal Transport with Landmark Constraints](https://mlsanity.com/paper/2608.19783/) (2026)

## Abstract (arXiv)

We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimensional manifold of diffeomorphisms. This optimal information transport, and modifications thereof, allows us to construct numerical algorithms for density matching. The algorithms are inherently more efficient than those based on optimal mass transport or diffeomorphic registration. Our methods have applications in medical image registration, texture mapping, image morphing, non-uniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.