In light of the need to both grow and diversify graduate enrollments in computing fields, this quantitative study examined variables associated with students' initial aspirations for computing graduate school as well as how aspirations were sustained or developed over time. Using a longitudinal sample of undergraduate students who enrolled in introductory computing courses at 15 research universities, findings suggest that environments and interactions that sustain undergraduate students' initial computing graduate aspirations are quite different than those that contribute to other students' development of graduate aspirations. Specifically, this study highlights the key role of domain-specific psychosocial beliefs (i.e., computing identity, computing self-efficacy) in shaping students' aspirations for graduate computing. Results also highlight important equity issues, particularly related to supporting graduate aspirations among underrepresented Students of Color in computing. We offer implications for cultivating gender and racial/ethnic diversity in computing graduate school pathways, which is imperative to generating more inclusive computing environments in the tech industry and academia.