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Face super-resolution is a domain-specific super-resolution task to generate a high-resolution facial image from a low-resolution one. In this paper, we propose a novel face super-resolution network, called CollageNet, to super-resolve an input image by exploiting a reference image of an identical person at the patch level. First, we extract feature pyramids from input and reference images to exploit multi-scale information hierarchically. Next, we compute the patch-wise similarities between input and reference feature pyramids and select the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> most similar reference patches to each input patch. Then, we compose a collaged feature pyramid by gluing those selected patches together. Finally, we obtain a super-resolved image by blending the collaged feature pyramid and the input feature. Experimental results demonstrate that the proposed CollageNet yields state-of-the-art performances.