  Nucleus instance segmentation in histology images is crucial for a broad
spectrum of clinical applications. Current dominant algorithms rely on
regression of nuclear proxy maps. Distinguishing nucleus instances from the
estimated maps requires carefully curated post-processing, which is error-prone
and parameter-sensitive. Recently, the Segment Anything Model (SAM) has earned
huge attention in medical image segmentation, owing to its impressive
generalization ability and promptable property. Nevertheless, its potential on
nucleus instance segmentation remains largely underexplored. In this paper, we
present a novel prompt-driven framework that consists of a nucleus prompter and
SAM for automatic nucleus instance segmentation. Specifically, the prompter
learns to generate a unique point prompt for each nucleus while the SAM is
fine-tuned to output the corresponding mask for the prompted nucleus.
Furthermore, we propose the inclusion of adjacent nuclei as negative prompts to
enhance the model's capability to identify overlapping nuclei. Without
complicated post-processing, our proposed method sets a new state-of-the-art
performance on three challenging benchmarks. Code is available at
\url{github.com/windygoo/PromptNucSeg}
