Optimal transport for deep generative models: State of the art and research challenges

Optimal transport has a long history in mathematics which was proposed by Gaspard Monge in the eighteenth century [Monge, 1781]. However, until recently, advances in optimal transport theory pave the way for its use in the AI community, particularly for formulating deep generative models. In this paper, we provide a comprehensive overview of the literature in the field of deep generative models using optimal transport theory with an aim of providing a systematic review as well as outstanding problems and more importantly, open research opportunities to use the tools from the established optimal transport theory in the deep generative model domain.