Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminator

Abstract: Generative Adversarial Networks (GANs) have shown great promise in modeling high dimensional data. The learning objective of GANs usually minimizes some measure discrepancy, \textit{e.g.}, $f$-divergence~($f$-GANs) or Integral Probability Metric~(Wasserstein GANs). With $f$-divergence as the objective function, the discriminator essentially estimates the density ratio, and the estimated ratio proves useful in further improving the sample quality of the generator. However, how to leverage the information contained in the discriminator of Wasserstein GANs (WGAN) is less explored. In this paper, we introduce the Discriminator Contrastive Divergence, which is well motivated by the property of WGAN's discriminator and the relationship between WGAN and energy-based model. Compared to standard GANs, where the generator is directly utilized to obtain new samples, our method proposes a semi-amortized generation procedure where the samples are produced with the generator's output as an initial state. Then several steps of Langevin dynamics are conducted using the gradient of the discriminator. We demonstrate the benefits of significant improved generation on both synthetic data and several real-world image generation benchmarks.