Existing retrieval-augmented generation (RAG) systems often assume that each query has a single correct answer. This assumption overlooks open-ended information-seeking scenarios where multiple plausible answers are valuable, and where diversity is important for creativity, fairness, and inclusive access to information. We show that standard RAG systems fail to fully use diverse retrieved contexts: simply increasing retrieval diversity does not necessarily lead to diverse generations. To address this limitation, we propose Diverge, a plug-and-play agentic RAG framework that improves the diversity--quality trade-off through iterative, reflection-guided exploration of diverse viewpoints and diversity-aware retrieval support. We further introduce evaluation metrics for characterizing the diversity-quality trade-off in open-ended question answering. Experiments across multiple real-world datasets and backbone LLMs show that Diverge achieves the best trade-off among competitive baselines, increasing diversity by $\sim2\times$ without noticeable quality degradation. These results reveal a systematic limitation of current RAGs and show the value of explicit diversity modeling.