  Stochastic generative models enable us to capture the geometric structure of
a data manifold lying in a high dimensional space through a Riemannian metric
in the latent space. However, its practical use is rather limited mainly due to
inevitable complexity. In this work we propose a surrogate conformal Riemannian
metric in the latent space of a generative model that is simple, efficient and
robust. This metric is based on a learnable prior that we propose to learn
using a basic energy-based model. We theoretically analyze the behavior of the
proposed metric and show that it is sensible to use in practice. We demonstrate
experimentally the efficiency and robustness, as well as the behavior of the
new approximate metric. Also, we show the applicability of the proposed
methodology for data analysis in the life sciences.
