Multiresolution mesh representations are a key tool used in computer graphics to achieve real-time interaction with large and complex object models. In a multiresolution modeling environment we are able to deal with global shape and structural details of the same object managing meshes of it at different level of refinement. We then need tools to coarsen a given fine mesh as well as tools for refining a coarse mesh. We study refinement approaches that combine the advantages of subdivision (arbitrary topology, local control and efficiency) with those of variational design (high quality surfaces). The basic idea behind this strategy, first proposed by Kobbelt and named variational subdivision, is to apply, at each subdivision step, a splitting operation to obtain a finer mesh followed by a smoothing operation to update the vertex mesh locations in order to increase the overall smoothness. In this research project the smoothing step is based on a geometric diffusion and filtering approach related to mean curvature motion, which have already been proved to be very promising for surface fairing purposes.