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Modeling sparse and dense image matching within a unified functional correspondence model has recently attracted increasing research interest. However, existing efforts mainly focus on improving matching accuracy while ignoring its efficiency, which is crucial for real-world applications. In this paper, we propose an efficient structure named Efficient Correspondence Transformer () by finding correspondences in a coarse-to-fine manner, which significantly improves the efficiency of functional correspondence model. To achieve this, multiple transformer blocks are stage-wisely connected to gradually refine the predicted coordinates upon a shared multi-scale feature extraction network. Given a pair of images and for arbitrary query coordinates, all the correspondences are predicted within a single feed-forward pass. We further propose an adaptive query-clustering strategy and an uncertainty-based outlier …