Extracting relations across large text spans has been relatively underexplored in NLP, but it is particularly important for high-value domains such as biomedicine, where obtaining high recall of the latest findings is crucial for practical applications. Compared to conventional information extraction confined to short text spans, document-level relation extraction faces additional challenges in both inference and learning. Given longer text spans, state-of-the-art neural architectures are less effective and task-specific self-supervision such as distant supervision becomes very noisy. In this paper, we propose decomposing document-level relation extraction into relation detection and argument resolution, taking inspiration from Davidsonian semantics. This enables us to incorporate explicit discourse modeling and leverage modular self-supervision for each sub-problem, which is less noise-prone and can be further refined end-to-end via variational EM. We conduct a thorough evaluation in biomedical machine reading for precision oncology, where cross-paragraph relation mentions are prevalent. Our method outperforms prior state of the art, such as multi-scale learning and graph neural networks, by over 20 absolute F1 points. The gain is particularly pronounced among the most challenging relation instances whose arguments never co-occur in a paragraph.