With the widespread application of Generative Artificial Intelligence (GAI) in education, promoting university students’ continuance intention (CI) to use such tools has become a pressing issue. Drawing upon the Expectation-Confirmation Model (ECM), this study incorporates two extended variables, AI Self-Efficacy (AI-SE) and AI Interaction Positivity (AIP), to construct a research model that explores the mechanisms underlying students’ continuance use of GAI. A questionnaire survey was conducted, yielding 144 valid responses from students across different Chinese universities. Data analysis was performed using SPSS and PLS-SEM to assess reliability, validity, and the structural model. The results indicate that Perceived Usefulness (PU) has a significant positive effect on both AI-SE and AIP. AI-SE not only significantly predicts AIP but also directly enhances CI, and further serves as a critical mediator between PU and CI. In contrast, the direct effect of AIP on CI was not statistically significant. These findings extend the applicability of ECM to the educational context of GAI, highlighting the central role of AI-SE in the formation of CI. Moreover, the study provides empirical evidence for educators and technology developers, suggesting that enhancing students’ perceptions of usefulness and strengthening their confidence in using GAI are essential to fostering long-term continuance intention.