Recent work has shown that the structure of deep convolutional neural networks can be used as a structured image prior for solving various inverse image restoration tasks. Instead of using hand-designed architectures, we propose to search for neural architectures that capture stronger image priors. Building upon a generic U-Net architecture, our core contribution lies in designing new search spaces for (1) an upsampling cell and (2) a pattern of cross-scale residual connections. We search for an improved network by leveraging an existing neural architecture search algorithm (using reinforcement learning with a recurrent neural network controller). We validate the effectiveness of our method via a wide variety of applications, including image restoration, dehazing, image-to-image translation, and matrix factorization. Extensive experimental results show that our algorithm performs favorably against state-of-the-art learning-free approaches and reaches competitive performance with existing learning-based methods in some cases.