Differences between novice and expert physics students have frequently been reported, yet students' development through intermediate stages has seldom been described. In this study, we characterize undergraduate physics majors' epistemological sophistication at various levels of degree progress. A cross-section of physics majors was surveyed with the Colorado Learning Attitudes about Science Survey. Beginning physics majors are significantly more expert-like than non-physics majors in introductory physics courses; furthermore, this high level of sophistication is constant over the first three years of the physics degree program, with increases at the senior and graduate levels. Based on longitudinal data on a subset of students, we observe negligible average shift in students' responses over periods of up to two years. We discuss implications for how and why physics students' epistemological sophistication develops, including a possible connection between CLASS survey response and self-identification as a physicist.