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We present a generative model and inference algorithm for 3D nonrigid object tracking. The model, which we call G-flow, enables the joint inference of 3D position, orientation, and nonrigid deformations, as well as object texture and background texture. Optimal inference under G-flow reduces to a conditionally Gaussian stochastic filtering problem. The optimal solution to this problem reveals a new space of computer vision algorithms, of which classic approaches such as optic flow and template matching are special cases that are optimal only under special circumstances. We evaluate G-flow on the problem of tracking facial expressions and head motion in 3D from single-camera video. Previously, the lack of realistic video data with ground truth nonrigid position information has hampered the rigorous evaluation of nonrigid tracking. We introduce a practical method of obtaining such ground truth data and present a new face video data set that was created using this technique. Results on this data set show that G-flow is much more robust and accurate than current deterministic optic-flow-based approaches.