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Limited by the cost and technology, the resolution of depth map collected by depth camera is often lower than that of its associated RGB camera. Although there have been many researches on RGB image super-resolution (SR), a major problem with depth map super-resolution is that there will be obvious jagged edges and excessive loss of details. To tackle these difficulties, in this work, we propose a multi-scale progressive fusion network for depth map SR, which possess an asymptotic structure to integrate hierarchical features in different domains. Given a low-resolution (LR) depth map and its associated high-resolution (HR) color image, We utilize two different branches to achieve multi-scale feature learning. Next, we propose a step-wise fusion strategy to restore the HR depth map. Finally, a multi-dimensional loss is introduced to constrain clear boundaries and details. Extensive experiments show that our proposed method produces improved results against state-of-the-art methods both qualitatively and quantitatively.