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Most existing action quality assessment methods rely on the deep features of an entire video to predict the score, which is less reliable due to the non-transparent inference process and poor interpretability. We argue that understanding both high-level semantics and internal temporal structures of actions in competitive sports videos is the key to making predictions accurate and interpretable. Towards this goal, we construct a new fine-grained dataset, called FineDiving, developed on diverse diving events with detailed annotations on action procedures. We also propose a procedure-aware approach for action quality assessment, learned by a new Temporal Segmentation Attention module. Specifically, we propose to parse pairwise query and exemplar action instances into consecutive steps with diverse semantic and temporal correspondences. The procedure-aware cross-attention is proposed to learn embeddings between query and exemplar steps to discover their semantic, spatial, and temporal correspondences, and further serve for fine-grained contrastive regression to derive a reliable scoring mechanism. Extensive experiments demonstrate that our approach achieves substantial improvements over state-of-the-art methods with better interpretability. The dataset and code are available at \url{https://github.com/xujinglin/FineDiving}.