Large language models (LLMs) are increasingly used not only for problem solving but also for creative ideation; however, generating ideas that are both novel and coherent remains challenging. While high-temperature sampling can promote originality, it often compromises consistency and usefulness. Here, we propose ReMIND, a four-stage framework comprising wake, which establishes a stable semantic baseline through low-temperature generation; dream, which performs high-temperature exploratory generation; judge, which evaluates candidate outputs for consistency and extracts salient novel ideas; and rewake, which consolidates selected ideas into coherent final outputs. By assigning these functions to independent LLM modules, ReMIND explicitly separates exploration from stabilization. We systematically evaluated diverse model configurations using multiple creative ideation tasks. External evaluations showed that novelty enhancement could emerge through two separable stages: first from the wake to the dream phase through high-temperature exploration, and subsequently from the dream to the rewake phase through judge-mediated selection and consolidation. Notably, different LLM families exhibited distinct functional tendencies. These findings suggest that serendipitous ideation in LLMs is not solely a property of individual models but emerges from interactions among models assigned to specialized cognitive roles. ReMIND provides a general framework for investigating computational creativity and demonstrates how modular LLM orchestration can bridge exploratory generation and coherent idea formation.

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