Abstract: Generative adversarial networks (GANs) play a minmax two-player game via adversarial training. The conventional understanding of adversarial training is that the discriminator is trained to estimate a divergence and the generator learns to minimize this divergence. We argue that despite the fact that many variants of GANs are developed following this paradigm, the existing theoretical understanding of GANs and the practical algorithms are inconsistent. In order to gain deeper theoretical insights and algorithmic inspiration for these GAN variants, we leverage Wasserstein gradient flows which characterize the evolution of particles in the sample space. Based on this, we introduce a unified generative modeling framework – MonoFlow: the particle evolution is rescaled via an arbitrary monotonically increasing mapping. Under our framework, adversarial training can be viewed as a procedure first obtaining MonoFlow's vector field via the discriminator and then the generator learns to parameterize the flow defined by the corresponding vector field. We also reveal the fundamental difference between variational divergence minimization and adversarial training. These analysis help us to identify what types of generator loss functions can lead to the successful training of GANs and suggest that GANs may have more loss designs beyond those developed in the literature, e.g., non-saturated loss, as long as they realize MonoFlow. Consistent empirical studies are also included to validate the effectiveness of our framework.
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