Large language models (LLMs) show strong potential to support creative tasks, but the role of the interface design is poorly understood. In particular, the effect of different modes of collaboration between humans and LLMs on co-creation outcomes is unclear. To test this, we conducted a randomized controlled experiment ($N = 486$) comparing: (a) two variants of reflective, human-led modes in which the LLM elicits elaboration through suggestions or questions, against (b) a proactive, model-led mode in which the LLM independently rewrites ideas. By assessing the effects on idea quality, diversity, and perceived ownership, we found that the model-led mode substantially improved idea quality but reduced idea diversity and users' perceived idea ownership. The reflective, human-led mode also improved idea quality, yet while preserving diversity and ownership. We independently validated the findings in a different context ($N = 640$). Our findings highlight the importance of designing interactions with generative AI systems as reflective thought partners that complement human strengths and augment creative processes.

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