We describe the relationship between gradient methods for computing optical flow and filter-based spatio-temporal energy models of biological motion processing, revealing that these techniques are equivalent under certain conditions. We discuss extensions of these techniques which compute probability distributions of optical flow. The use of distributions allows proper handling of the uncertainties inherent in the optical flow computation, facilitating the combination with information from other sources. The probabilistic framework also leads to several useful extensions of the standard quadratic gradient solution. We use these extensions to compute optical flow for both a synthetic and a real image sequence.