There is an ongoing debate in higher education about the value of broad programmes versus specialised programmes. Educational professionals argue that students use the space provided by broad programmes to develop interests in diverse domains, while the scope of specialised programmes allows students to converge in interests. The present study investigates whether students enrolled in broad and specialised programmes indeed differ in how their interests develop. To do so, we traced the interest development of 124 Dutch students from their final year in secondary education until the end of their first year in higher education. We used an experience sampling method to measure students' momentary interests over a week and repeated this every three months. For each data collection week, we coded in how many different domains students were interested, and subsequently ran a multigroup, sequential, latent growth curve model. We found that students in broad programmes develop more divergent interests, while students in specialised programmes develop more convergent interests. This shows how students use the space provided by programmes to shape their interests. Our results can help higher education institutes in discussing whether a more diverse or focused curriculum is desirable from a societal and student perspective.