  Standard formulations of GANs, where a continuous function deforms a
connected latent space, have been shown to be misspecified when fitting
different classes of images. In particular, the generator will necessarily
sample some low-quality images in between the classes. Rather than modifying
the architecture, a line of works aims at improving the sampling quality from
pre-trained generators at the expense of increased computational cost. Building
on this, we introduce an additional network to predict latent importance
weights and two associated sampling methods to avoid the poorest samples. This
idea has several advantages: 1) it provides a way to inject disconnectedness
into any GAN architecture, 2) since the rejection happens in the latent space,
it avoids going through both the generator and the discriminator, saving
computation time, 3) this importance weights formulation provides a principled
way to reduce the Wasserstein's distance to the target distribution. We
demonstrate the effectiveness of our method on several datasets, both synthetic
and high-dimensional.
