The recent surge in generative artificial intelligence (AI) applications within engineering design requires equipping future engineers with the skills to effectively utilize these advanced design tools. Understanding how students think about generative AI in design is pivotal in shaping engineering design education. This study aims to explore mechanical engineering students’ perceptions and approaches to generative design (GD) compared to parametric design (PD) and traditional design (TD). To achieve this, a comprehensive curriculum encompassing these three design paradigms was developed and administered to seven undergraduate mechanical engineering students. Students engaged with the curriculum activities while their responses and interactions were recorded using a verbal protocol. Three students were selected for an in-depth multi-case study analysis. The qualitative and quantitative findings suggest that students’ thought processes and behaviors in GD are influenced and informed by their experiences and understanding of TD and PD.