The ability to understand and predict molecular responses towards external perturbations is a core question in molecular biology. Technological advancements in the recent past have enabled the generation of high-resolution single-cell data, making it possible to profile individual cells under different experimentally controlled perturbations. However, cells are typically destroyed during measurement, resulting in unpaired distributions over either perturbed or non-perturbed cells. Leveraging the theory of optimal transport and the recent advents of convex neural architectures, we learn a coupling describing the response of cell populations upon perturbation, enabling us to predict state trajectories on a single-cell level.We apply our approach, CellOT, to predict treatment responses of 21,650 cells subject to four different drug perturbations. CellOT outperforms current state-of-the-art methods both qualitatively and quantitatively, accurately capturing cellular behavior shifts across all different drugs.