We introduce a parametric nonlinear transformation for jointly Gaussianizing patches of natural images. The transformation is differentiable, can be efficiently inverted, and thus induces a density model. It generalizes and performs better than several previous image models such as ICA, radial Gaussianization, and ISA. Model samples are visually similar to natural image patches. We use the model for image restoration, and show that it can be cascaded to build nonlinear hierarchies analogous to multiscale representations.