Abstract Most of the current face hallucination methods, whether they are shallow learning-based or deep learning-based, all try to learn a relationship model between Low-Resolution (LR) and HighResolution (HR) spaces with the help of a training set. They mainly focus on modeling image prior through either model-based optimization or discriminative inference learning. However, when the input LR face is tiny, the learned prior knowledge is no longer effective and their performance will drop sharply. To solve this problem, in this paper we propose a general face hallucination method that can integrate model-based optimization and discriminative inference. In particular, to exploit the model based prior, the Deep Convolutional Neural Networks (CNN) denoiser prior is plugged into the super-resolution optimization model with the aid of image-adaptive Laplacian regularization. Additionally, we further develop a highfrequency details compensation method by dividing the face image to facial components and performing face hallucination in a multi-layer neighbor embedding manner. Experiments demonstrate that the proposed method can achieve promising super-resolution results for tiny input LR faces.