A Bayesian ensemble learning method is introduced for unsupervised extraction of dynamic processes from noisy data. The data are assumed to be generated by an unknown nonlinear mapping from unknown factors. The dynamics of the factors are modeled using a nonlinear state-space model. The nonlinear mappings in the model are represented using multilayer perceptron networks. The proposed method is computationally demanding, but it allows the use of higher-dimensional nonlinear latent variable models than other existing approaches. Experiments with chaotic data show that the new method is able to blindly estimate the factors and the dynamic process that generated the data. It clearly outperforms currently available nonlinear prediction techniques in this very difficult test problem.