As artificial intelligence (AI) continues to evolve, particularly in the context of generative art, a critical question emerges about the future role of human creativity: In the age of generative AI, does individual creative ability still matter? Here, we explored this question via an online, pre-registered study involving 375 participants who completed gold-standard divergent-thinking tasks and generated semantic wordsets for AI-art creation using an AI-art generator. We generated the resultant images from these participant-produced wordsets through DALL-E, and a group of trained raters independently assessed the images for general creativity. Findings revealed widespread positive correlations among the creativity tasks. Specifically, the semantic diversity of wordsets and performance on the gold-standard creativity tasks served as significant positive predictors for the creativity of the AI-generated images, indicating that individuals possessing greater divergent-thinking capabilities, and who generated more-creative word prompts for an art generator, produced more-creative AI-generated artwork. These results suggest that, despite the democratizing effect of AI-art generation, human creativity remains an important component in directing AI-produced creative outcomes like visual art. The implications of these findings are discussed in the context of creative industries and the science of creativity.