Constructing effective and generalizable synthesized motions is crucial for creating naturalistic, versatile, and effective virtual characters and robots. High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. I would like to go through several existing models such as Gaussian Process Dynamic Systems and Deep Belief Networks. I would analyze their strengths and limitations. I would also try to incorporate physical constraints to improve the motion quality. And on the other hand, try to improve the structure of the models or the learning algorithms.