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TITLE: Various Formulations of Optimal Transport Problems and Its Application to Generative Modeling

ABSTRACT: The Optimal Transport (OT) problem aims to find a transport map that connects two distributions while minimizing a specified cost function. This concept has been applied to generative modeling by utilizing OT between tractable prior distributions and real data. In this presentation, we introduce various OT problems and their application to generative modeling. Specifically, we emphasize the Unbalanced Optimal Transport (UOT) problem, which exhibits robustness against outliers compared to traditional OT methods. Furthermore, we provide brief overviews of other OT-related generative models, such as the JKO-based model and Schrodinger bridge matching. Additionally, we explore OT applications in various vision tasks, including image-to-image translation, image restoration, and domain adaptation.