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Assessing action quality from videos has attracted growing attention in recent years. Most existing approaches usually tackle this problem based on regression algorithms, which ignore the intrinsic ambiguity in the score labels caused by multiple judges or their subjective appraisals. To address this issue, we propose an uncertainty-aware score distribution learning (USDL) approach for action quality assessment (AQA). Specifically, we regard an action as an instance associated with a score distribution, which describes the probability of different evaluated scores. Moreover, under the circumstance where fine-grained score labels are available (e.g., difficulty degree of an action or multiple scores from different judges), we further devise a multi-path uncertainty-aware score distributions learning (MUSDL) method to explore the disentangled components of a score. We conduct experiments on three AQA datasets containing various Olympic actions and surgical activities, where our approaches set new state-of-the-arts under the Spearman's Rank Correlation. 1 * indicates equal contribution, the corresponding author is Jiwen Lu.