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Point clouds upsampling is a challenging issue to generate dense and uniform point clouds from the given sparse input. Most existing methods either take the end-to-end supervised learning based manner, where large amounts of pairs of sparse input and dense ground-truth are exploited as supervision information; or treat up-scaling of different scale factors as independent tasks, and have to build multiple networks to handle upsampling with varying factors. In this paper, we propose a novel approach that achieves self-supervised and magnification-flexible point clouds upsampling simultaneously. We formulate point clouds upsampling as the task of seeking nearest projection points on the implicit surface for seed points. To this end, we define two implicit neural functions to estimate projection direction and distance respectively, which can be trained by two pretext learning tasks. Experimental results demonstrate that our self-supervised learning based scheme achieves competitive or even better performance than supervised learning based state-of-the-art methods. The source code is publicly available at https://github.com/xnowbzhao/sapcu.