This paper presents a method to simultaneously regularize diffusion weighted images and their estimated diffusion tensors, with the goal of suppressing noise and restoring tensor information. We enforce a data fidelity constraint, using coupled robust anisotropic diffusion filters, to ensure consistency of the restored diffusion tensors with the regularized diffusion weighted images. The filters are designed to take advantage of robust statistics and to be adopted to the anisotropic nature of diffusion tensors, which can effectively keep boundaries between piecewise constant regions in the tensor volume and also the diffusion weighted images during the regularized process. To facilitate Euclidean operations on the diffusion tensors, log-Euclidean metrics are adopted when performing the filtering. Experimental results on simulated and real image data demonstrate the effectiveness of the proposed method.