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.

本文提出了一种在生成对抗网络中产生直接能量估计样本的方法，并证明该方法不仅可以确保生成器收敛到真实数据分布，而且还能使辨别器在全局最优时保留密度信息。我们推导出所引入解决方案的解析形式，并分析其性质。为了使所提出的框架在实践中可训练，我们引入了两种有效的近似技术。实验结果与理论分析紧密匹配，证明辨别器能够恢复数据分布的能量。