We propose a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). In our framework, we define a discretization inspired by a distribution-dependent ordinary differential equation (ODE). We show that such a discretization is convergent and propose a viable class of adversarial training methods to implement this discretization, which we call W1 Forward Euler (W1-FE). In particular, the ODE framework allows us to implement persistent training, a novel training technique that cannot be applied to typical WGAN algorithms without the ODE interpretation. Remarkably, when we do not implement persistent training, we prove that our algorithms simplify to existing WGAN algorithms; when we increase the level of persistent training appropriately, our algorithms outperform existing WGAN algorithms in both low- and high-dimensional examples.

翻译：我们提出了一种新的理论视角来审视Wasserstein生成对抗网络（WGANs）。在该框架中，我们定义了一种受分布依赖常微分方程（ODE）启发的离散化方法。我们证明了此类离散化具有收敛性，并提出了一类可行的对抗训练方法来实现该离散化，我们将其称为W1前向欧拉法（W1-FE）。特别地，ODE框架使我们能够实现持续训练——这是一种在没有ODE解释时无法应用于典型WGAN算法的新型训练技术。值得注意的是，当不采用持续训练时，我们证明所提算法可简化为现有WGAN算法；而当适当增强持续训练强度时，我们的算法在低维与高维示例中均优于现有WGAN算法。