Teaching business process improvement is important as it is the most value adding activity in the process lifecycle. Unlike for other lifecycle stages, however, the related body of knowledge on how to actually improve a process is still light on sound, replicable methods. This challenge increases if explorative BPM is the desired subject of study. Motivated by this context, this paper reports on the experiences of an MBA unit called Business Process Design with a focus on comparing students' responses with the explorative process design space as created by generative AI. The results show that the manually created diversity of explorative BPM ideas needs to be augmented by the related capabilities of generative AI to arrive at a comprehensive process design space. This paper provides advice for BPM educators for how to teach augmented, explorative process design. Besides its value as a guide for lecturers teaching BPM, this paper inspires augmented process exploration as a subject of interest for future BPM research.