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Generating diverse, interesting responses to chitchat conversations is a problem for neural conversational agents. This paper makes two substantial contributions to improving diversity in dialogue generation. First, we propose a novel metric which uses Natural Language Inference (NLI) to measure the semantic diversity of a set of model responses for a conversation. We evaluate this metric using an established framework (Tevet and Berant, 2021) and find strong evidence indicating NLI Diversity is correlated with semantic diversity. Specifically, we show that the contradiction relation is more useful than the neutral relation for measuring this diversity and that incorporating the NLI model’s confidence achieves state-of-the-art results. Second, we demonstrate how to iteratively improve the semantic diversity of a sampled set of responses via a new generation procedure called Diversity Threshold Generation, which results in an average 137% increase in NLI Diversity compared to standard generation procedures.