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Image smoothing is a fundamental low-level vision task that aims to preserve salient structures of an image while removing insignificant details. Deep learning has been explored in image smoothing to deal with the complex entanglement of semantic structures and trivial details. However, current methods neglect two important facts in smoothing: 1) naive pixel-level regression supervised by the limited number of high-quality smoothing ground-truth could lead to domain shift and cause generalization problems towards real-world images; 2) texture appearance is closely related to object semantics, so that image smoothing requires awareness of semantic difference to apply adaptive smoothing strengths. To address these issues, we propose a novel Contrastive Semantic-Guided Image Smoothing Network (CSGIS-Net) that combines both contrastive prior and semantic prior to facilitate robust image smoothing. The supervision signal is augmented by leveraging undesired smoothing effects as negative teachers, and by incorporating segmentation tasks to encourage semantic distinctiveness. To realize the proposed network, we also enrich the original VOC dataset with texture enhancement and smoothing labels, namely VOC-smooth, which first bridges image smoothing and semantic segmentation. Extensive experiments demonstrate that the proposed CSGIS-Net outperforms state-of-the-art algorithms by a large margin. Code and dataset are available at https://github.com/wangjie6866/CSGIS-Net.