Generative AI applications present unique design challenges. As generative AI technologies are increasingly being incorporated into mainstream applications, there is an urgent need for guidance on how to design user experiences that foster effective and safe use. We present six principles for the design of generative AI applications that address unique characteristics of generative AI UX and offer new interpretations and extensions of known issues in the design of AI applications. Each principle is coupled with a set of design strategies for implementing that principle via UX capabilities or through the design process. The principles and strategies were developed through an iterative process involving literature review, feedback from design practitioners, validation against real-world generative AI applications, and incorporation into the design process of two generative AI applications. We anticipate the principles to usefully inform the design of generative AI applications by driving actionable design recommendations.