  Autoencoders are important generative models that, among others, have the
ability to interpolate image sequences. However, interpolated images are
usually not semantically meaningful.In this paper, motivated by dynamic optimal
transport, we consider image interpolation as a mass transfer problem and
propose a novel regularization term to penalize non-smooth and unrealistic
changes in the interpolation result. Specifically, we define the path energy
function for each path connecting the source and target images. The autoencoder
is trained to generate the $L^2$ optimal transport geodesic path when decoding
a linear interpolation of their latent codes. With a simple extension, this
model can handle complicated environments, such as allowing mass transfer
between obstacles and unbalanced optimal transport. A key feature of the
proposed method is that it is physics-driven and can generate robust and
realistic interpretation results even when only very limited training data are
available.
