  The underlying geometrical structure of the latent space in deep generative
models is in most cases not Euclidean, which may lead to biases when comparing
interpolation capabilities of two models. Smoothness and plausibility of linear
interpolations in latent space are associated with the quality of the
underlying generative model. In this paper, we show that not all such
interpolations are comparable as they can deviate arbitrarily from the shortest
interpolation curve given by the geodesic. This deviation is revealed by
computing curve lengths with the pull-back metric of the generative model,
finding shorter curves than the straight line between endpoints, and measuring
a non-zero relative length improvement on this straight line. This leads to a
strategy to compare linear interpolations across two generative models. We also
show the effect and importance of choosing an appropriate output space for
computing shorter curves. For this computation we derive an extension of the
pull-back metric.
