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In this paper, we investigate the training process of generative networksthat use a type of probability density distance named particle-based distanceas the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. However, theseGANs often suffer from the problem of unstable training. In this paper, weanalyze the stability of the training process of these GANs from theperspective of probability density dynamics. In our framework, we regard thediscriminator $D$ in these GANs as a feature transformation mapping that mapshigh dimensional data into a feature space, while the generator $G$ maps randomvariables to samples that resemble real data in terms of feature space. Thisperspective enables us to perform stability analysis for the training of GANsusing the Wasserstein gradient flow of the probability density function. Wefind that the training process of the discriminator is usually unstable due tothe formulation of $\min_G \max_D E(G, D)$ in GANs. To address this issue, weadd a stabilizing term in the discriminator loss function. We conductexperiments to validate our stability analysis and stabilizing method.

Stability Analysis Framework for Particle-based Distance GANs with Wasserstein Gradient Flow