Selecting optimal models and hyperparameters is crucial for accurate optical-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyperparameters, and the prior and likelihood motion models. Inference is performed on each of the three levels of this so-defined hierarchical model by maximization of marginalized a posteriori probability distribution functions. In particular, the first level is used to achieve motion estimation in a classical a posteriori scheme. By marginalizing out the motion variable, the second level enables to infer regularization coefficients and hyperparameters of non-Gaussian M-estimators commonly used in robust statistics. The last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data. The method is evaluated on image sequences of fluid flows and from the "Middlebury" database. Experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state-of-the-art methods.