  In this paper, we propose to equip Generative Adversarial Networks with the
ability to produce direct energy estimates for samples.Specifically, we propose
a flexible adversarial training framework, and prove this framework not only
ensures the generator converges to the true data distribution, but also enables
the discriminator to retain the density information at the global optimal. We
derive the analytic form of the induced solution, and analyze the properties.
In order to make the proposed framework trainable in practice, we introduce two
effective approximation techniques. Empirically, the experiment results closely
match our theoretical analysis, verifying the discriminator is able to recover
the energy of data distribution.
