Research idea innovation is a fundamental engine of scientific progress, yet it remains difficult to generate and evaluate in a scalable and controllable way. This challenge lies in its inherently open-ended and multi-objective nature, where ideas should balance novelty, plausibility and feasibility. While recent LLM-based approaches have made progress through carefully designed prompts or agent pipelines, they are constrained by predefined, static ideation workflows. To address this limitation, we propose MindFlow, a framework that explicitly formulates ideation as a graph-structured Flow in Mind, which is composed of modular thinking operators and modeled by a probabilistic mind supernet. Given a research topic, a controller dynamically samples thinking flows to generate candidate ideas. This open-ended problem is optimized using a tournament-based relative ranking, enabling the controller to progressively favor higher-quality thinking flows. We further introduce an evaluation protocol that jointly assesses problem finding and problem solving, going beyond title- or abstractonly judgments. Across diverse topics, MindFlow shows its superiority as an explicit, controllable and optimizable research idea innovator.
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