We present an algorithm for creating high resolution anatomically plausible images consistent with acquired clinical brain MRI scans with large inter-slice spacing. Although large data sets of clinical images contain a wealth of information, time constraints during acquisition result in sparse scans that fail to capture much of the anatomy. These characteristics often render computational analysis impractical as many image analysis algorithms tend to fail when applied to such images. Highly specialized algorithms that explicitly handle sparse slice spacing do not generalize well across problem domains. In contrast, we aim to enable application of existing algorithms that were originally developed for high resolution research scans to significantly undersampled scans. We introduce a generative model that captures fine-scale anatomical structure across subjects in clinical image collections and derive an algorithm for filling in the missing data in scans with large inter-slice spacing. Our experimental results demonstrate that the resulting method outperforms state-of-the-art upsampling super-resolution techniques, and promises to facilitate subsequent analysis not previously possible with scans of this quality. Our implementation is freely available at https://github.com/adalca/papago.