  In implicit models, one often interpolates between sampled points in latent
space. As we show in this paper, care needs to be taken to match-up the
distributional assumptions on code vectors with the geometry of the
interpolating paths. Otherwise, typical assumptions about the quality and
semantics of in-between points may not be justified. Based on our analysis we
propose to modify the prior code distribution to put significantly more
probability mass closer to the origin. As a result, linear interpolation paths
are not only shortest paths, but they are also guaranteed to pass through
high-density regions, irrespective of the dimensionality of the latent space.
Experiments on standard benchmark image datasets demonstrate clear visual
improvements in the quality of the generated samples and exhibit more
meaningful interpolation paths.
