The conventional understanding of adversarial training in generative adversarial networks (GANs) 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 were developed following this paradigm, the current theoretical understanding of GANs and their practical algorithms are inconsistent. In this paper, we leverage Wasserstein gradient flows which characterize the evolution of particles in the sample space, to gain theoretical insights and algorithmic inspiration of GANs. We introduce a unified generative modeling framework - MonoFlow: the particle evolution is rescaled via a monotonically increasing mapping of the log density ratio. Under our framework, adversarial training can be viewed as a procedure first obtaining MonoFlow's vector field via training the discriminator and the generator learns to draw the particle flow defined by the corresponding vector field. We also reveal the fundamental difference between variational divergence minimization and adversarial training. This analysis helps 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 the literature (e.g., non-saturated loss), as long as they realize MonoFlow. Consistent empirical studies are included to validate the effectiveness of our framework.

翻译：传统上，生成对抗网络（GANs）的对抗训练被视为判别器学习估计散度、生成器最小化该散度的过程。本文认为，尽管众多GAN变体遵循此范式发展，但当前GAN的理论认知与其实际算法存在不一致性。我们利用描述样本空间粒子演化的Wasserstein梯度流，为GANs提供理论洞见与算法启发。本文提出统一生成建模框架MonoFlow：通过对数密度比的单调递增映射重新缩放粒子演化。在此框架下，对抗训练可被理解为：首先通过训练判别器获得MonoFlow的向量场，随后生成器学习绘制该向量场所定义的粒子流。我们同时揭示了变分散度最小化与对抗训练之间的根本差异。该分析有助于甄别何种损失函数能促使GANs成功训练，并表明只要实现MonoFlow机制，GANs的损失设计可超越现有文献（例如非饱和损失）的范畴。我们通过一致性的实证研究验证了该框架的有效性。