  We present a framework to understand GAN training as alternating density
ratio estimation and approximate divergence minimization. This provides an
interpretation for the mismatched GAN generator and discriminator objectives
often used in practice, and explains the problem of poor sample diversity. We
also derive a family of generator objectives that target arbitrary
$f$-divergences without minimizing a lower bound, and use them to train
generative image models that target either improved sample quality or greater
sample diversity.
