The goal of this work is to efficiently identify visually similar patterns in images, e.g. identifying an artwork detail copied between an engraving and an oil painting, or recognizing parts of a night-time photograph visible in its daytime counterpart. Lack of training data is a key challenge for this co-segmentation task. We present a simple yet surprisingly effective approach to overcome this difficulty: we generate synthetic training pairs by selecting segments in an image and copy-pasting them into another image. We then learn to predict the repeated region masks. We find that it is crucial to predict the correspondences as an auxiliary task and to use Poisson blending and style transfer on the training pairs to generalize on real data. We analyse results with two deep architectures relevant to our joint image analysis task: a transformer-based architecture and Sparse Nc-Net, a recent network designed to predict coarse correspondences using 4D convolutions. We show our approach provides clear improvements for artwork details retrieval on the Brueghel dataset and achieves competitive performance on two place recognition benchmarks, Tokyo247 and Pitts30K. We also demonstrate the potential of our approach for unsupervised image collection analysis by introducing a spectral graph clustering approach to object discovery and demonstrating it on the object discovery dataset of \cite{rubinstein2013unsupervised} and the Brueghel dataset. Our code and data are available at http://imagine.enpc.fr/~shenx/SegSwap/.