Abstract: Humans are able to segment images effortlessly without supervision using perceptual grouping. Here, we propose a counter-intuitive computational approach to solving unsupervised perceptual grouping and segmentation: that they arise *because* of neural noise, rather than in spite of it. We (1) mathematically demonstrate that under realistic assumptions, neural noise can be used to separate objects from each other; (2) that adding noise in a DNN enables the network to segment images even though it was never trained on any segmentation labels; and (3) that segmenting objects using noise results in segmentation performance that aligns with the perceptual grouping phenomena observed in humans, and is sample-efficient. We introduce the Good Gestalt (GG) datasets --- six datasets designed to specifically test perceptual grouping, and show that our DNN models reproduce many important phenomena in human perception, such as illusory contours, closure, continuity, proximity, and occlusion. Finally, we (4) show that our model improves performance on our GG datasets compared to other tested unsupervised models by $24.9$%. Together, our results suggest a novel unsupervised segmentation method requiring few assumptions, a new explanation for the formation of perceptual grouping, and a novel potential benefit of neural noise.