While systems that use Artificial Intelligence (AI) are increasingly becoming part of everyday technology use, we do not fully understand how AI changes design processes. A structured understanding of how designers work with AI is needed to improve the design process and educate future designers. To that end, we conducted interviews with designers who participated in projects which used AI. While past work focused on AI systems created by experienced designers, we focus on the perspectives of a diverse sample of interaction designers. Our results show that the design process of an interactive system is affected when AI is integrated and that design teams adapt their processes to accommodate AI. Based on our data, we contribute four approaches adopted by interaction designers working with AI: a priori, post-hoc, model-centric, and competence-centric. Our work contributes a pragmatic account of how design processes for AI systems are enacted.