IdeaBlocks: Expressing and Reusing Divergent Intents for Graphic Design Exploration using Generative AI

While designers increasingly leverage Generative AI for divergent exploration, current interaction is optimized for convergent refinement, forcing users to specify fixed targets rather than open-ended search spaces. Based on a formative study (N=7), we define the anatomy of Divergent Intent, comprising property, direction, and range, and identified two critical barriers: the lack of mechanisms to explicitly shape the parametric boundaries of exploration and the difficulty of reusing successful search strategies. We present IdeaBlocks, where users can modularize divergent intents into Exploration Blocks. Users can reuse prior intents at multiple levels (block, path, and project) with options for literal or context-adaptive reuse. In our comparative study (N=12), participants using IdeaBlocks explored 2.13 times more images with 12.5% greater visual diversity than the baseline, demonstrating how structured intent expression and reuse support effective divergence. A three-day deployment study (N=6) further revealed how different reuse mechanisms allowed distinct creative strategies, offering design implications for future intent-aware creativity supports.