Dialogue systems pretrained with large language models generate locally coherent responses, but lack the fine-grained control over responses necessary to achieve specific goals. A promising method to control response generation is exemplar-based generation, in which models edit exemplar responses that are retrieved from training data, or hand-written to strategically address discourse-level goals, to fit new dialogue contexts. But, current exemplar-based approaches often excessively copy words from the exemplar responses, leading to incoherent replies. We present an Exemplar-based Dialogue Generation model, EDGE, that uses the semantic frames present in exemplar responses to guide generation. We show that controlling dialogue generation based on the semantic frames of exemplars, rather than words in the exemplar itself, improves the coherence of generated responses, while preserving semantic meaning and conversation goals present in exemplar responses.