A Differential Equation Approach for Wasserstein GANs and Beyond
Keywords: Generative modelling, finite elements, gradient flow, persistent training
Abstract: This paper proposes a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). To minimize the Wasserstein-1 distance between the true data distribution and our estimate of it, we derive a distribution-dependent ordinary differential equation (ODE), which represents the gradient flow of the Wasserstein-1 loss, and show that a forward Euler discretization of the ODE converges. This inspires a new class of generative models that naturally integrates persistent training (which we call W1-FE). When persistent training is turned off, we prove that W1-FE reduces to WGAN. When we intensify persistent training appropriately, W1-FE is shown to outperform WGAN in training experiments from low to high dimensions, in terms of both convergence speed and training results.
Primary Area: generative models
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Submission Number: 1162
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