Optical Flow estimation in noisy image sequences requires a special denoising strategy. Towards this end we introduce a new tensor-driven anisotropic diffusion scheme which is designed to enhance optical-flow-like spatiotemporal structures. This is achieved by selecting diffusivities in a special manner depending on the eigenvalues of the well known structure tensor. We illustrate how the proposed choice differs from edge- and coherence-enhancing anisotropic diffusion. Furthermore we extend a recently discovered discretization scheme for anisotropic diffusion to 3D data. An automatic stop criterion to terminate the diffusion after a suitable time is given. The performance of the introduced method is examined quantitatively using image sequences with a substantial amount of noise added.