This paper describes a method for high-quality depth superresolution. The standard formulations of image-guided depth upsampling, using simple joint filtering or quadratic optimization, lead to texture copying and depth bleeding artifacts. These artifacts are caused by inherent discrepancy of structures in data from different sensors. Although there exists some correlation between depth and intensity discontinuities, they are different in distribution and formation. To tackle this problem, we formulate an optimization model using a nonconvex regularizer. A nonlocal affinity established in a high-dimensional feature space is used to offer precisely localized depth boundaries. We show that the proposed method iteratively handles differences in structure between depth and intensity images. This property enables reducing texture copying and depth bleeding artifacts significantly on a variety of range data sets. We also propose a fast alternating direction method of multipliers algorithm to solve our optimization problem. Our solver shows a noticeable speed up compared with the conventional majorize-minimize algorithm. Extensive experiments with synthetic and real-world data sets demonstrate that the proposed method is superior to the existing methods.