This paper investigates the potential impact of deep generative models on the work of creative professionals, specifically focusing on fashion design. We argue that current generative modeling tools lack critical features that would make them useful creativity support tools, and introduce our own tool, generative.fashion1, which was designed with theoretical principles of design space exploration in mind. Through qualitative studies with fashion design apprentices, we demonstrate how generative.fashion supported both divergent and convergent thinking, and compare it with a state-of-the-art diffusion model, Stable Diffusion. In general, the apprentices preferred generative.fashion over Stable Diffusion, citing the features explicitly designed to support ideation. We conclude that the exploration and development of novel interfaces and interaction modalities that are theoretically aligned with principles of design space exploration is crucial for unlocking the creative potential of generative AI and advancing a new era of creativity.