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：传统观点认为，生成对抗网络中对抗训练的核心是判别器学习估计散度，而生成器则致力于最小化该散度。我们指出，尽管大量生成对抗网络变体遵循这一范式，但当前对生成对抗网络的理论理解与实际算法之间仍存在不一致性。本文借助瓦瑟斯坦梯度流（用于刻画样本空间中粒子演化过程）为生成对抗网络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标定。在该框架下，对抗训练可被视作先通过判别器训练获取MonoFlow的向量场，再由生成器学习绘制该向量场对应的粒子流。同时，我们揭示了变分散度最小化与对抗训练的根本差异。该分析有助于识别何种生成器损失函数能实现生成对抗网络的有效训练，并表明只要能够实现MonoFlow，生成对抗网络可能拥有超越现有文献（如非饱和损失）的更多损失函数设计方案。我们通过一致性实验验证了所提框架的有效性。