In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. However, these GANs often suffer from the problem of unstable training. In this paper, we analyze the stability of the training process of these GANs from the perspective of probability density dynamics. In our framework, we regard the discriminator $D$ in these GANs as a feature transformation mapping that maps high dimensional data into a feature space, while the generator $G$ maps random variables to samples that resemble real data in terms of feature space. This perspective enables us to perform stability analysis for the training of GANs using the Wasserstein gradient flow of the probability density function. We find that the training process of the discriminator is usually unstable due to the formulation of $\min_G \max_D E(G, D)$ in GANs. To address this issue, we add a stabilizing term in the discriminator loss function. We conduct experiments to validate our stability analysis and stabilizing method.

翻译：本文研究了以粒子距离（如MMD GAN、Cramér GAN、EIEG GAN）为目标的生成网络训练过程。然而，这类生成对抗网络常面临训练不稳定的问题。本文从概率密度动力学角度分析了这些生成对抗网络的训练稳定性。在所提出的框架中，我们将生成对抗网络中的判别器$D$视为将高维数据映射到特征空间的特征变换映射，而生成器$G$则将随机变量映射为在特征空间上接近真实数据的样本。这一视角使我们可以利用概率密度函数的Wasserstein梯度流对生成对抗网络的训练进行稳定性分析。我们发现，由于生成对抗网络采用$\min_G \max_D E(G, D)$的优化形式，判别器的训练过程通常是不稳定的。为解决这一问题，我们在判别器损失函数中增加了稳定项。我们通过实验验证了稳定性分析及所提出的稳定化方法的有效性。