Deep Generative Wasserstein Gradient Flows

Deep generative modeling is a rapidly-advancing field with a wealth of modeling choices developed in the past decades. Amongst them, Wasserstein gradient flows (WGF) are a powerful and theoretically rich class of methods. However, their applications to high-dimensional distributions remain relatively underexplored. In this paper, we present Deep Generative Wasserstein Gradient Flows (DGGF), which constructs a WGF between two distributions by minimizing the entropy-regularized $f$-divergence. We demonstrate how to train a deep density ratio estimator that is required for the WGF and apply it to the task of generative modeling. Experiments demonstrate that DGGF is able to synthesize high-fidelity images of resolutions up to $128\times128$, directly in data space. We demonstrate that DGGF has an interpretable diagnostic of sample quality by naturally estimating the KL divergence throughout the gradient flow. Finally, we show DGGF's modularity by composition with external density ratio estimators for conditional generation, as well as for unpaired image-to-image translation with no modifications to the framework.