# A geometric perspective on regularized optimal transport

arXiv: https://arxiv.org/abs/1703.10243 · HTML: https://mlsanity.com/paper/1703.10243/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [On the Hopf-Cole Transform for Control-affine Schr"odinger Bridge](https://mlsanity.com/paper/2503.17640/) (2025)
- [HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models](https://mlsanity.com/paper/2409.09614/) (2024)

## Abstract (arXiv)

We present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schr"odinger bridge problem and the Yasue problem. We also propose an analogue of the Hopf--Cole transformation in the geometric setting.