Super-resolution microscopy methods (e.g. STORM or PALM imaging) have become essential tools in biology, opening up a va- riety of new questions that were previously inaccessible with standard light microscopy methods. In this paper we develop new Bayesian image processing methods that extend the reach of super-resolution mi- croscopy even further. Our method couples variational inference techniques with a data summarization based on Laplace approxi- mation to ensure computational scalability. Our formulation makes it straightforward to incorporate prior information about the underlying sample to further improve ac- curacy. The proposed method obtains dra- matic resolution improvements over previ- ous methods while retaining computational tractability.