Recent years have witnessed increasing attention on the application of graph alignment to on-Web tasks, such as knowledge graph integration and social network linking. Despite achieving remarkable performance, prevailing graph alignment models still suffer from noisy supervision, yet how to mitigate the impact of noise in labeled data is still under-explored. The negative sampling based noise discrimination model has been a feasible solution to detect the noisy data and filter them out. However, due to its sensitivity to the sampling distribution, the negative sampling based noise discrimination model would lead to an inaccurate decision boundary. Furthermore, it is difficult to find an abiding threshold to separate the potential positive (benign) and negative (noisy) data in the whole training process. To address these important issues, in this paper, we design a non-sampling discrimination model resorting to the unbiased risk estimation of positive-unlabeled learning to circumvent the harmful impact of negative sampling. We also propose to select the appropriate potential positive data at different training stages by an adaptive filtration threshold enabled by curriculum learning, for maximally improving the performance of alignment model and non-sampling discrimination model. Extensive experiments conducted on several real-world datasets validate the effectiveness of our proposed method.