This paper proposes a novel method for deblurring facial images to recognize faces degraded by blur. The main problem is how to infer a point spread function (PSF) representing the process of blur. Inferring a PSF from a single facial image is an ill-posed problem. To make this problem more tractable, our method uses learned prior information derived from a training set of blurred facial images of several individuals. We construct a feature space such that blurred faces degraded by the same PSF are similar to one another and form a cluster. During training, we compute a statistical model of each PSF cluster in this feature space. For PSF inference we compare a query image of unknown blur with each model and select the closest one. Using the PSF corresponding to that model, the query image is deblurred, ready for recognition. Experiments on a standard face database artificially degraded by focus or motion blur show that our method substantially improves the recognition performance compared with state-of-the-art methods. We also demonstrate improved performance on real blurred images.