Discourse relations bind smaller linguistic units into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked arguments. A more subtle challenge is that it is not enough to represent the meaning of each argument of a discourse relation, because the relation may depend on links between lower-level components, such as entity mentions. Our solution computes distributional meaning representations by composition up the syntactic parse tree. A key difference from previous work on compositional distributional semantics is that we also compute representations for entity mentions, using a novel downward compositional pass. Discourse relations are predicted from the distributional representations of the arguments, and also of their coreferent entity mentions. The resulting system obtains substantial improvements over the previous state-of-the-art in predicting implicit discourse relations in the Penn Discourse Treebank.