A generative model based on the gaussian mixture model and gaussian processes is presented in this paper. Typical motion paths are learnt and then used for motion prediction using this model. The principal novel aspect of this approach is the modelling of paths using gaussian processes. It allows the representation of smooth trajectories and avoids discretization problems found in most existing methods. Gaussian processes not only provides a comprehensive and formal theoretical framework to work with, it also lends itself naturally to path clustering using gaussian mixture models. Learning is performed using expectation maximization where the E-Step uses variational methods to maximize its lower bound before optimization over parameters are performed in the M-Step.