In most professional cinema productions, the color palette of the movie is painstakingly adjusted by a team of skilled colorists -- through a process referred to as color grading -- to achieve a certain visual look. The time and expertise required to grade a video makes it difficult for amateurs to manipulate the colors of their own video clips. In this work, we present a method that allows a user to transfer the color palette of a model video clip to their own video sequence. We estimate a per-frame color transform that maps the color distributions in the input video sequence to that of the model video clip. Applying this transformation naively leads to artifacts such as bleeding and flickering. Instead, we propose a novel differential-geometry-based scheme that interpolates these transformations in a manner that minimizes their curvature, similarly to curvature flows. In addition, we automatically determine a set of keyframes that best represent this interpolated transformation curve, and can be used subsequently, to manually refine the color grade. We show how our method successfully transfer color palettes between videos for a range of visual styles and a number of input video clips.