# Wasserstein-Fisher-Rao Splines

arXiv: https://arxiv.org/abs/2203.15728 · HTML: https://mlsanity.com/paper/2203.15728/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 6 of 6)

- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Trajectory Inference with Smooth Schr"odinger Bridges](https://mlsanity.com/paper/2503.00530/) (2025)
- [Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging](https://mlsanity.com/paper/2405.19679/) (2024)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport](https://mlsanity.com/paper/2601.06810/) (2026)
- [Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference](https://mlsanity.com/paper/2610.19878/) (2026)

## Abstract (arXiv)

We study interpolating splines on the Wasserstein-Fisher-Rao (WFR) space of measures with differing total masses. To achieve this, we derive the covariant derivative and the curvature of an absolutely continuous curve in the WFR space. We prove that this geometric notion of curvature is equivalent to a Lagrangian notion of curvature in terms of particles on the cone. Finally, we propose a practical algorithm for computing splines extending the work of arXiv:2010.12101.