In this paper, a Bayesian super resolution (SR) method obtains high resolution (HR) brain Diffusion-Weighted Magnetic Resonance Imaging (DMRI) images from degraded low resolution (LR) images. Under a Bayesian formulation, the unknown HR image, the acquisition process and the unknown parameters are modeled as stochastic processes. The likelihood model is modeled using a Gaussian distribution to estimate the error between the a linear representation and the observations. The prior is introduced as a Multivariate Gaussian Distribution, for which the inverse of the covariance matrix is approximated by Laplacian-like functions that model the local relationships, capturing thereby non-homogeneous relationships between neighbor intensities. Experimental results show the method outperforms the base line by 2.56 dB when using PSNR as a metric of quality in a set of 35 cases.