  We consider distance functions between conditional distributions functions.
We focus on the Wasserstein metric and its Gaussian case known as the Frechet
Inception Distance (FID).We develop conditional versions of these metrics, and
analyze their relations. Then, we numerically compare the metrics inthe context
of performance evaluation of conditional generative models. Our results show
that the metrics are similar in classical models which are less susceptible to
conditional collapse. But the conditional distances are more informative in
modern unsuper-vised, semisupervised and unpaired models where learning the
relations between the inputs and outputs is the main challenge.
