We report on the dynamics of confined zero-dimensional polaritons. We excite resonantly discrete polariton states optically with a tailored picosecond laser pulse and observe their emission time resolved in the two-dimensional k space or real space. We are able to distinguish between three regimes. When the laser excites only one state no dynamics are observed. When a small number of well separated states are excited, the dynamics are described in terms of interference. When a quasicontinuum of states is excited, the dynamics are described in terms of ballistically propagating two-dimensional (2D) polaritons which scatter elastically at the potential barriers. The measured propagation velocities are reproduced with the theory of 2D polaritons, which sustains our interpretation.