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：生成对抗网络中对抗训练的传统理解认为，判别器被训练以估计散度，而生成器则学习最小化该散度。本文指出，尽管众多GAN变体遵循这一范式开发，但当前GAN的理论理解与实际算法之间存在不一致。我们利用刻画样本空间中粒子演化的Wasserstein梯度流，为GAN提供理论洞见与算法启发。我们提出统一生成建模框架——MonoFlow：粒子演化通过对数密度比的单调递增映射进行重新缩放。在该框架下，对抗训练可视为先通过训练判别器获取MonoFlow的向量场，然后生成器学习绘制由该向量场所定义的粒子流。我们还揭示了变分散度最小化与对抗训练之间的根本差异。这一分析有助于识别何种类型的生成器损失函数能实现GAN的成功训练，并表明只要实现MonoFlow，GAN可拥有文献之外更多的损失设计（例如非饱和损失）。我们包含了一致的实证研究以验证该框架的有效性。