We present COD3S, a novel method for generating semantically diverse sentences using neural sequence-to-sequence (seq2seq) models. Conditioned on an input, seq2seq models typically produce semantically and syntactically homogeneous sets of sentences and thus perform poorly on one-to-many sequence generation tasks. Our two-stage approach improves output diversity by conditioning generation on locality-sensitive hash (LSH)-based semantic sentence codes whose Hamming distances highly correlate with human judgments of semantic textual similarity. Though it is generally applicable, we apply COD3S to causal generation, the task of predicting a propositions plausible causes or effects. We demonstrate through automatic and human evaluation that responses produced using our method exhibit improved diversity without degrading task performance.