Card et al.'s classic paper "The Design Space of Input Devices" established the value of design spaces as a tool for HCI analysis and invention. We posit that developing design spaces for emerging pre-trained, generative AI models is necessary for supporting their integration into human-centered systems and practices. We explore what it means to develop an AI model design space by proposing two design spaces relating to generative AI models: the first considers how HCI can impact generative models (i.e., interfaces for models) and the second considers how generative models can impact HCI (i.e., models as an HCI prototyping material).