This paper develops a statistical inference approach, Bayesian Tensor Inference, for style transformation between photo images and sketch images of human faces. Motivated by the rationale that image appearance is determined by two cooperative factors: image content and image style, we first model the interaction between these factors through learning a patch-based tensor model. Second, by introducing a common variation space, we capture the inherent connection between photo patch space and sketch patch space, thus building bidirectional mapping/inferring between the two spaces. Subsequently, we formulate a Bayesian approach accounting for the statistical inference from sketches to their corresponding photos in terms of the learned tensor model. Comparative experiments are conducted to contrast the proposed method with state-of-the-art algorithms for facial sketch synthesis in a novel face hallucination scenario: sketch-based facial photo hallucination. The encouraging results obtaine...