Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs

Alessandro Scagliotti, Sara Farinelli

In this paper, we consider the problem of recovering the $W_2$-optimal transport map T between absolutely continuous measures $\hat{I}¼,\hat{I}½\in \mathcal{P}({\mathbb{R}}^n)$ as the flow of a l…