We introduce MOVE, a novel method to segment objects without any form ofsupervision. MOVE exploits the fact that foreground objects can be shiftedlocally relative to their initial position and result in realistic(undistorted) new images. This property allows us to train a segmentation modelon a dataset of images without annotation and to achieve state of the art(SotA) performance on several evaluation datasets for unsupervised salientobject detection and segmentation. In unsupervised single object discovery,MOVE gives an average CorLoc improvement of 7.2% over the SotA, and inunsupervised class-agnostic object detection it gives a relative AP improvementof 53% on average. Our approach is built on top of self-supervised features(e.g. from DINO or MAE), an inpainting network (based on the MaskedAutoEncoder) and adversarial training.