# Light Entropic Optimal Transport on Riemannian Manifolds

arXiv: https://arxiv.org/abs/2610.03085 · HTML: https://mlsanity.com/paper/2610.03085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 20 of 20)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [Plugin Estimation of Smooth Optimal Transport Maps](https://mlsanity.com/paper/2107.12364/) (2021)
- [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Entropic Neural Optimal Transport via Diffusion Processes](https://mlsanity.com/paper/2211.01156/) (2022)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Riemannian Convex Potential Maps](https://mlsanity.com/paper/2106.10272/) (2021)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [Entropic Riemannian Neural Optimal Transport](https://mlsanity.com/paper/2605.04255/) (2026)

## Abstract (arXiv)

Entropic Optimal Transport (EOT) has become a practical framework for learning stochastic couplings between complex distributions, with applications in generative modeling and domain adaptation. However, most EOT solvers are designed for Euclidean spaces, while manifold extensions remain limited and often rely on costly iterative methods, simulated dynamics, or generic neural models that do not fully exploit the underlying geometry. We introduce ManifoldLightOT, a light approach for learning kernel-induced EOT couplings directly on common manifolds. Using the kernel form of the EOT solution, we construct geometry-specific Gibbs kernels together with compatible potential parameterizations for spheres, tori, SO(3), and SE(3). These choices yield closed-form normalization and directly sampleable conditional distributions. Our formulation naturally extends to products of manifolds, making it applicable to more complex geometries. The parameters of the potentials are optimized directly from samples using Monte Carlo estimates of the learning objective. Through synthetic and real-world experiments, we show that ManifoldLightOT often outperforms existing manifold OT methods while retaining direct sampling.