This article addresses the problem of coherent change detection in repeat-pass synthetic aperture radar (SAR) imagery. A Bayesian approach is formulated as an alternative to conventional window-based change detection statistics that entail losses to spatial resolution. The proposed approach assigns prior distributions to the unobserved model variables to exploit spatial structure both in the geophysical scattering qualities of the scene and among the scene disturbances that take place between the passes. Variational expectation maximization is used to efficiently approximate the posterior distribution of the latent variables and the prior model hyperparameters. Experiments on simulated and measured interferometric SAR data pairs indicate the effectiveness of the proposed change detection method and highlight improvements over traditional window-based approaches.