Constructing 3D representations of object geometry is critical for many downstream manipulation tasks. These representations must be built from potentially noisy partial observations. In this work we focus on the problem of reconstructing a multi-object scene from a single RGBD image. Current deep learning approaches to this problem can be brittle to noisy real world observations and out-of-distribution objects. Other approaches that do not rely on training data cannot accurately infer the backside of objects. We propose BRRP, a reconstruction method that can leverage preexisting mesh datasets to build an informative prior during robust probabilistic reconstruction. In order to make our method more efficient, we introduce the concept of retrieval-augmented prior, where we retrieve relevant components of our prior distribution during inference. Our method produces a distribution over object shape that can be used for reconstruction or measuring uncertainty. We evaluate our method in both procedurally generated scenes and in real world scenes. We show our method is more robust than a deep learning approach while being more accurate than a method with an uninformative prior.