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This fact occurs for depth estimation based on either monocular or stereo, with the latter often providing a valid source of self-supervision for the former. In contrast, to soften typical stereo artefacts, we propose a novel self-supervised paradigm reversing the link between the two. Purposely, in order to train deep stereo networks, we distill knowledge through a monocular completion network. This architecture exploits single-image clues and few sparse points, sourced by traditional stereo algorithms, to estimate dense yet accurate disparity maps by means of a consensus mechanism over multiple estimations. We thoroughly evaluate with popular stereo datasets the impact of different supervisory signals showing how stereo networks trained with our paradigm outperform existing self-supervised frameworks. Finally, our proposal achieves notable generalization capabilities dealing with domain shift issues. 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