Removing noisy links from an observed network is a task commonly required for preprocessing real-world network data. However, containing both noisy and clean links, the observed network cannot be treated as a trustworthy information source for supervised learning. Therefore, it is necessary but also technically challenging to detect noisy links in the context of data contamination. To address this issue, in the present article, a two-phased computational model is proposed, called link-information augmented twin autoencoders, which is able to deal with: 1) link information augmentation; 2) link-level contrastive denoising; 3) link information correction. Extensive experiments on six real-world networks verify that the proposed model outperforms other comparable methods in removing noisy links from the observed network so as to recover the real network from the corrupted one very accurately. Extended analyses also provide interpretable evidence to support the superiority of the proposed model for the task of network denoising.