Time-of-flight point cloud acquisition systems have grown in precision and robustness over the past few years. However, even subtle motion can induce significant distortions due to the long acquisition time. In contrast, there exists sensors that produce depth maps at a higher frame rate, but they suffer from low resolution and accuracy. In this paper, we correct distortions produced by small motions in time-of-flight acquisitions and even output a corrected animated sequence by combining a slow but high-resolution time-of-flight LiDAR system and a fast but low-resolution consumer depth sensor. We cast the problem as a curve-to-volume registration, by seeing a LiDAR point cloud as a curve in a 4-dimensional spacetime and the captured low-resolution depth video as a 4-dimensional spacetime volume. Our approach starts by registering both captured sequences in 4D, in a coarse-to-fine approach. It then computes an optical flow between the low-resolution frames and finally transfers high-resolution details by advecting along the flow. We demonstrate the efficiency of our approach on both synthetic data, on which we can compute registration errors, and real data.