Large language models are transforming the creative process by offering unprecedented capabilities to algorithmically generate ideas. While these tools can enhance human creativity when people cocreate with them, it’s unclear how this will impact unassisted human creativity. We conducted two large pre-registered parallel experiments involving 1,100 participants attempting tasks targeting the two core components of creativity, divergent and convergent thinking. We compare the effects of two forms of large language model (LLM) assistance—a standard LLM providing direct answers and a coach-like LLM offering guidance—with a control group receiving no AI assistance, and focus particularly on how all groups perform in a final, unassisted stage. Our findings reveal that while LLM assistance can provide short-term boosts in creativity during assisted tasks, it may inadvertently hinder independent creative performance when users work without assistance, raising concerns about the long-term impact on human creativity and cognition.