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Full-reference (FR) image quality assessment (IQA) evaluates the visual quality of a distorted image by measuring its perceptual difference with pristine-quality reference, and has been widely used in low-level vision tasks. Pairwise labeled data with mean opinion score (MOS) are required in training FR-IQA model, but is time-consuming and cumbersome to collect. In contrast, unlabeled data can be easily collected from an image degradation or restoration process, making it encouraging to exploit unlabeled training data to boost FR-IQA performance. Moreover, due to the distribution inconsistency between labeled and unlabeled data, outliers may occur in unlabeled data, further increasing the training difficulty. In this paper, we suggest to incorporate semi-supervised and positive-unlabeled (PU) learning for exploiting unlabeled data while mitigating the adverse effect of outliers. Particularly, by treating all labeled data as positive samples, PU learning is leveraged to identify negative samples (i.e., outliers) from unlabeled data. Semi-supervised learning (SSL) is further deployed to exploit positive unlabeled data by dynamically generating pseudo-MOS. We adopt a dual-branch network including reference and distortion branches. Furthermore, spatial attention is introduced in the reference branch to concentrate more on the informative regions, and sliced Wasserstein distance is used for robust difference map computation to address the misalignment issues caused by images recovered by GAN models. Extensive experiments show that our method performs favorably against state-of-the-arts on the benchmark datasets PIPAL, KADID-10k, TID2013, LIVE and CSIQ.