  It can be difficult to tell whether a trained generative model has learned to
generate novel examples or has simply memorized a specific set of outputs. In
published work, it is common to attempt to address this visually, for example
by displaying a generated example and its nearest neighbor(s) in the training
set (in, for example, the L2 metric). As any generative model induces a
probability density on its output domain, we propose studying this density
directly. We first study the geometry of the latent representation and
generator, relate this to the output density, and then develop techniques to
compute and inspect the output density. As an application, we demonstrate that
"memorization" tends to a density made of delta functions concentrated on the
memorized examples. We note that without first understanding the geometry, the
measurement would be essentially impossible to make.
