Creativity, one of the cornerstones of students' 21st-century skills, is regarded as an important learning outcome of science, technology, engineering, arts, and mathematics (STEAM) education. Meanwhile, problem-based digital making (DM), which combines the child-friendly programming activities of DM with problem-solving elements, is an emerging instructional design to facilitate STEAM learning. This qualitative case study examines the implementation of a problem-based DM instructional program that used the block-based programming tool Scratch to cultivate the participants' creativity. Fifty-four middle school students (aged 10-14 years) in Hong Kong participated in the program, which totaled 10 contact hours over five consecutive weeks. Through triangulating students' DM artifacts, video recordings, field notes, and interviews, the researchers characterized the students' creative expression, examined the role of problem-based DM in encouraging creative work, and investigated the use of Scratch for mediating student creativity. The results showed that problem-based DM activities fostered students' creative expressions in the dimensions of novelty, utility, aesthetics, and authenticity. While Scratch mediated the way the students presented their solutions, it had limitations that hindered the students' digital artifact construction. The findings provide theoretical insights for framing creativity and offer practical implications for the implementation of problem-based DM in K-12 contexts.