We introduce a strategy for learning image registration without imaging data, producing powerful networks agnostic to magnetic resonance imaging (MRI) contrast. While classical methods accurately estimate the spatial correspondence between images, they solve an optimization problem for every new image pair. Learning methods are fast at test time but limited to images with contrasts and geometric content seen at training. We propose to remove this dependency using a generative strategy that exposes networks to a wide range of synthetic images during training, forcing them to generalize. We show that networks trained within this framework generalize to a broad array of unseen MRI contrasts and surpass the state of the art brain registration accuracy for any contrast combination tested. Critically, training on shapes synthesized from noise distributions results in competitive performance, removing the dependency on acquired data of any kind. However, if available, synthesizing images from anatomical labels can further boost accuracy.