Applications that could benefit from automatic understanding of human-human conversations often come with challenges associated with private information in real-world data such as call center or clinical conversations. Working with protected data also increases costs of annotation, which limits technology development. To address these challenges, we propose DIALGEN, a human-in-the-loop semi-automated dialogue generation framework. DIALGEN uses a language model (ChatGPT) that can follow schema and style specifications to produce fluent conversational text, generating a complex conversation through iteratively generating subdialogues and using human feedback to correct inconsistencies or redirect the flow. In experiments on structured summarization of agent-client information gathering calls, framed as dialogue state tracking, we show that DIALGEN data enables significant improvement in model performance.