Abstract: Given a document and a target aspect (e.g., a topic of interest), aspect-based abstractive summarization attempts to generate a summary with respect to the aspect. Previous studies usually assume a small pre-defined set of aspects and fall short of summarizing on other diverse topics. In this work, we study summarizing on \emph{arbitrary} aspects relevant to the document, which significantly expands the application of the task in practice. Due to the lack of supervision data, we develop a new weak supervision construction method and an aspect modeling scheme, both of which integrate rich external knowledge sources such as ConceptNet and Wikipedia. Experiments show our approach achieves performance boosts on summarizing both real and synthetic documents given pre-defined or arbitrary aspects.