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Image inpainting is the task of filling masked or unknown regions of an image with visually realistic contents, which has been remarkably improved by Deep Neural Networks (DNNs) recently. Essentially, as an inverse problem, the inpainting has the underlying challenges of reconstructing semantically coherent results without texture artifacts. Many previous efforts have been made via exploiting attention mechanisms and prior knowledge, such as edges and semantic segmentation. However, these works are still limited in practice by an avalanche of learnable prior parameters and prohibitive computational burden. To this end, we propose a novel model -- Wavelet prior attention learning in Axial Inpainting Network (WAIN), whose generator contains the encoder, decoder, as well as two key components of Wavelet image Prior Attention (WPA) and stacked multi-layer Axial-Transformers (ATs). Particularly, the WPA guides the high-level feature aggregation in the multi-scale frequency domain, alleviating the textual artifacts. Stacked ATs employ unmasked clues to help model reasonable features along with low-level features of horizontal and vertical axes, improving the semantic coherence. Extensive quantitative and qualitative experiments on Celeba-HQ and Places2 datasets are conducted to validate that our WAIN can achieve state-of-the-art performance over the competitors. The codes and models will be released.