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We introduce a novel probabilistic approach for non-parametric nonrigid image registration using generalized elastic nets, a model previously used for topographic maps. The idea of the algorithm is to adapt an elastic net (a constrained Gaussian mixture) in the spatial-intensity space of one image to fit the second image. The resulting net directly represents the correspondence between image pixels in a probabilistic way and recovers the underlying image deformation. We regularize the net with a differential prior and develop an efficient optimization algorithm using linear conjugate gradients. The nonparametric formulation allows for complex transformations having local deformation. The method is generally applicable to registering point sets of arbitrary features. The accuracy and effectiveness of the method are demonstrated on different medical image and point set registration examples with locally nonlinear underlying deformations.