This paper presents a novel approach to modeling the pos terior distribution in image registration that is computationally efficient for large deformation diffeomorphic metric mapping (LDDMM). We develop a Laplace approximation of Bayesian registration models entirely in a bandlimited space that fully describes the properties of diffeomorphic transformations. In contrast to current methods, we compute the inverse Hessian at the mode of the posterior distribution of diffeomorphisms directly in the low dimensional frequency domain. This dramatically reduces the computational complexity of approximating posterior marginals in the high dimensional imaging space. Experimental results show that our method is significantly faster than the state-of-the-art diffeomorphic image registration uncertainty quantification algorithms, while producing comparable results. The efficiency of our method strengthens the feasibility in prospective clinical applications, e.g., real- time image-guided navigation for brain surgery.