There has been a growing interest in multiscale resolution of nonlinear data in recent years. A significant issue therein is smoothness. We consider subdivision of manifold valued data. The notion of those subdivision schemes based on an appropriate linear one will be in a general setting such that known examples like subdividing by means of geodesic averaging in Riemannian manifolds, log-exponential subdivision schemes in Lie groups and those induced in symmetric spaces are covered. We investigate smoothness of these constructions and analyze applications to dynamics of rigid body and diffusion tensors.