We study the problems of upsampling a low-resolution depth map and interpolating an initial set of sparse motion matches, with the guidance from a corresponding high-resolution color image. The common objective for both tasks is to densify a set of sparse data points, either regularly distributed or scattered, to a full image grid through a 2D guided interpolation process. We propose a unified approach that casts the fundamental guided interpolation problem into a hierarchical, global optimization framework. Built on a weighted least squares (WLS) formulation with its recent fast solver–fast global smoothing (FGS) technique, our method progressively densifies the input data set by efficiently performing the cascaded, global interpolation (or smoothing) with alternating guidances. Our cascaded scheme effectively addresses the potential structure inconsistency between the sparse input data and the guidance image, while preserving depth or motion boundaries. To prevent new data points of low confidence from contaminating the next interpolation process, we also prudently evaluate the consensus of the interpolated intermediate data. Experiments show that our general interpolation approach successfully tackles several notorious challenges. Our method achieves quantitatively competitive results on various benchmark evaluations, while running much faster than other competing methods designed specifically for either depth upsampling or motion interpolation.