Fault localization in the nation's power grid networks is known to be challenging, due to the massive scale and inherent complexity. In this study, we model the phasor angles across the buses as a Gaussian Markov random field (GMRF), where the partial correlation coefficients of GMRF are quantified in terms of the physical parameters of power systems. We then take the GMRF-based approach for fault diagnosis, through change detection and localization in the partial correlation matrix of GMRF. Specifically, we take advantage of the topological hierarchy of power systems, and devise a multi-resolution inference algorithm for fault localization, in a distributed manner. Simulation results are used to demonstrate the effectiveness of the proposed approach.