In this paper we present an unsupervised differential-geometric approach for learning Riemannian metrics for dynamical models. Given a training set of models the optimal metric is selected among a family of pullback metrics induced by the Fisher information tensor through a parameterized diffeomorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then be posed on the learnt manifold. Experimental results concerning action and identity recognition based on simple scalar features are shown, proving how learning a metric actually improves classification rates when compared with Fisher geodesic distance and other classical distance functions.