Coupled aspect-opinion extraction aims to identify aspect-opinion pairs in the form of (aspect term, opinion term) or triplets in the form of (aspect term, opinion term, sentiment polarity) from user-generated texts. Compared to the traditional aspect-based sentiment prediction or extraction tasks, coupled aspect-opinion extraction needs to associate aspects with their corresponding opinions and organize opinion-related information into structured outputs. The existing works either divide this task into subproblems (i.e., term extraction and relation prediction) or utilize a unified tagging scheme. However, these methods only focus on atomic word-level interactions and ignore the intensive information propagation among different granularities (e.g., words and word pairs). To address this limitation, we propose a progressive multigranularity information propagation network that progressively explores three types of correlations with different granularities. Specifically, our model starts with the most basic word-level correlations by composing all possible word pairs. In the second stage, the pairwise relation information is used to update the word features. The last stage propagates information among word pairs to produce the relation scores. We treat the task as a unified relation prediction problem and construct an end-to-end framework that iteratively conducts the three-stage information propagation to refine the textual representations. Comprehensive experiments on different aspect-based sentiment analysis benchmarks clearly demonstrate the effectiveness of the proposed approach.