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We present a theoretical and computational framework for nonrigid multimodal registration. We proceed by minimization of statistical similarity criteria (global and local) in a variational framework, and use the corresponding gradients to drive a flow of diffeomorphisms allowing large deformations. This flow is introduced through a new template propagation method, by composition of small displacements. Regularization is performed using fast filtering techniques. This approach yields robust matching algorithms offering a good computational efficiency. We apply this method to compensate distortions between EPI images (fMRI) and anatomical MRI volumes.