Extractive summarization aims to form a summary by directly extracting sentences from the source document. Existing works mostly formulate it as a sequence labeling problem by making individual sentence label predictions. This paper proposes DiffuSum, a novel paradigm for extractive summarization, by directly generating the desired summary sentence representations with diffusion models and extracting sentences based on sentence representation matching. In addition, DiffuSum jointly optimizes a contrastive sentence encoder with a matching loss for sentence representation alignment and a multi-class contrastive loss for representation diversity. Experimental results show that DiffuSum achieves the new state-of-the-art extractive results on CNN/DailyMail with ROUGE scores of $44.83/22.56/40.56$. Experiments on the other two datasets with different summary lengths also demonstrate the effectiveness of DiffuSum. The strong performance of our framework shows the great potential of adapting generative models for extractive summarization. To encourage more following work in the future, we have released our codes at \url{https://github.com/hpzhang94/DiffuSum}
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