In many fields, self-supervised learning solutions are rapidly evolving and\nfilling the gap with supervised approaches. This fact occurs for depth\nestimation based on either monocular or stereo, with the latter often providing\na valid source of self-supervision for the former. In contrast, to soften\ntypical stereo artefacts, we propose a novel self-supervised paradigm reversing\nthe link between the two. Purposely, in order to train deep stereo networks, we\ndistill knowledge through a monocular completion network. This architecture\nexploits single-image clues and few sparse points, sourced by traditional\nstereo algorithms, to estimate dense yet accurate disparity maps by means of a\nconsensus mechanism over multiple estimations. We thoroughly evaluate with\npopular stereo datasets the impact of different supervisory signals showing how\nstereo networks trained with our paradigm outperform existing self-supervised\nframeworks. Finally, our proposal achieves notable generalization capabilities\ndealing with domain shift issues. Code available at\nhttps://github.com/FilippoAleotti/Reversing\n