  Although machine learning models trained on massive data have led to
break-throughs in several areas, their deployment in privacy-sensitive domains
remains limited due to restricted access to data. Generative models trained
with privacy constraints on private data can sidestep this challenge, providing
indirect access to private data instead. We propose DP-Sinkhorn, a novel
optimal transport-based generative method for learning data distributions from
private data with differential privacy. DP-Sinkhorn minimizes the Sinkhorn
divergence, a computationally efficient approximation to the exact optimal
transport distance, between the model and data in a differentially private
manner and uses a novel technique for control-ling the bias-variance trade-off
of gradient estimates. Unlike existing approaches for training differentially
private generative models, which are mostly based on generative adversarial
networks, we do not rely on adversarial objectives, which are notoriously
difficult to optimize, especially in the presence of noise imposed by privacy
constraints. Hence, DP-Sinkhorn is easy to train and deploy. Experimentally, we
improve upon the state-of-the-art on multiple image modeling benchmarks and
show differentially private synthesis of informative RGB images. Project
page:https://nv-tlabs.github.io/DP-Sinkhorn.
