Partial label learning (PLL) is a typical weakly supervised learning, where each sample is associated with a set of candidate labels. The basic assumption of PLL is that the ground-truth label must reside in the candidate set. However, this assumption may not be satisfied due to the unprofessional judgment of the annotators, thus limiting the practical application of PLL. In this paper, we relax this assumption and focus on a more general problem, noisy PLL, where the ground-truth label may not exist in the candidate set. To address this challenging problem, we further propose a novel framework called "Automatic Refinement Network (ARNet)". Our method consists of multiple rounds. In each round, we purify the noisy samples through two key modules, i.e., noisy sample detection and label correction. To guarantee the performance of these modules, we start with warm-up training and automatically select the appropriate correction epoch. Meanwhile, we exploit data augmentation to further reduce prediction errors in ARNet. Through theoretical analysis, we prove that our method is able to reduce the noise level of the dataset and eventually approximate the Bayes optimal classifier. To verify the effectiveness of ARNet, we conduct experiments on multiple benchmark datasets. Experimental results demonstrate that our ARNet is superior to existing state-of-the-art approaches in noisy PLL. Our code will be made public soon.