  We propose a new algorithm that uses an auxiliary neural network to express
the potential of the optimal transport map between two data distributions. In
the sequel, we use the aforementioned map to train generative networks. Unlike
WGANs, where the Euclidean distance is ${\it implicitly}$ used, this new method
allows to ${\it explicitly}$ use ${\it any}$ transportation cost function that
can be chosen to match the problem at hand. For example, it allows to use the
squared distance as a transportation cost function, giving rise to the
Wasserstein-2 metric for probability distributions, which results in fast and
stable gradient descends. It also allows to use image centered distances, like
the structure similarity index, with notable differences in the results.
