Rich and diverse knowledge bases (KB) are foundational building blocks for online knowledge sharing communities such as StackOverflow and Quora, and applications such as conversational assistants (aka chatbots). A popular format for knowledge bases is question-answer pairs (or FAQs), where questions are designed to accurately match a multitude of queries. In this paper, we address the problem of automatic creation of such Q&A-based knowledge bases from domain-specific, long-form textual content (e.g., web articles). Specifically, we consider the problem of question generation, which is the task of generating questions given a paragraph of text as input, with a goal to achieve both diversity and fidelity of the generated questions. Towards this goal we propose PROTEGE, a diverse question generation framework which consists of (1) a novel encoder-decoder based Large Language Model (LLM) architecture which can take a variety of prompts and generate a diverse set of candidate questions, and (2) a hill-climbing algorithm that maximizes a sub-modular objective function to balance diversity with fidelity. Through our experiments on three popular public Q&A datasets, we demonstrate that PROTEGE improves diversity by +16% and fidelity by +8% over diverse beam search and prompt-based baselines.