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Semantic segmentation is an important and prevalent task, but severely suffers from the high cost of pixel-level annotations when extending to more classes in wider applications. To this end, we focus on the problem named weak-shot semantic segmentation, where the novel classes are learnt from cheaper image-level labels with the support of base classes having off-the-shelf pixel-level labels. To tackle this problem, we propose SimFormer, which performs dual similarity transfer upon MaskFormer. Specifically, MaskFormer disentangles the semantic segmentation task into two sub-tasks: proposal classification and proposal segmentation for each proposal. Proposal segmentation allows proposal-pixel similarity transfer from base classes to novel classes, which enables the mask learning of novel classes. We also learn pixel-pixel similarity from base classes and distill such class-agnostic semantic similarity to the semantic masks of novel classes, which regularizes the segmentation model with pixel-level semantic relationship across images. In addition, we propose a complementary loss to facilitate the learning of novel classes. Comprehensive experiments on the challenging COCO-Stuff-10K and ADE20K datasets demonstrate the effectiveness of our method. Codes are available at https://github.com/bcmi/SimFormer-Weak-Shot-Semantic-Segmentation.