The recently proposed facial cloaking attacks add invisible perturbation (cloaks) to facial images to protect users from being recognized by unauthorized facial recognition models. However, we show that the "cloaks" are not robust enough and can be removed from images. This paper introduces PuFace, an image purification system leveraging the generalization ability of neural networks to diminish the impact of cloaks by pushing the cloaked images towards the manifold of natural (uncloaked) images before the training process of facial recognition models. Specifically, we devise a purifier that takes all the training images including both cloaked and natural images as input and generates the purified facial images close to the manifold where natural images lie. To meet the defense goal, we propose to train the purifier on particularly amplified cloaked images with a loss function that combines image loss and feature loss. Our empirical experiment shows PuFace can effectively defend against two state-of-the-art facial cloaking attacks and reduces the attack success rate from 69.84\% to 7.61\% on average without degrading the normal accuracy for various facial recognition models. Moreover, PuFace is a model-agnostic defense mechanism that can be applied to any facial recognition model without modifying the model structure.