  Generative deep neural networks used in machine learning, like the
Variational Auto-Encoders (VAE), and Generative Adversarial Networks (GANs)
produce new objects each time when asked to do so with the constraint that the
new objects remain similar to some list of examples given as input. However,
this behavior is unlike that of human artists that change their style as time
goes by and seldom return to the style of the initial creations.
  We investigate a situation where VAEs are used to sample from a probability
measure described by some empirical dataset.
  Based on recent works on Radon-Sobolev statistical distances, we propose a
numerical paradigm, to be used in conjunction with a generative algorithm, that
satisfies the two following requirements: the objects created do not repeat and
evolve to fill the entire target probability distribution.
