Curvature flows can be seen as a type of heat equation and depending on the curvature terms being considered, it can model a variety of smoothing behavior. From a computational perspective, one needs to approximate surfaces appropriately and many powerful and sophisticated methods have been developed to describe and model such flows on the CPU. The GPU on the other hand offers immense parallel computational power together with a large local memory bandwidth, and is quickly becoming the de-facto inexpensive solution to many problems. However, understanding the implications of parallel architectures is crucial in optimizing many of the algorithms. For computational geometry processing, many of the algorithms are still too slow on the CPU for practical considerations. Thus the aim of this project will be to analyze and optimize the discrete curvature flow methods and implement them on the GPU. This work can be seen at the interface of differential geometric analysis (curvature flows etc.), together with the discrete geometry and geometry processing as well as scientific visualization.