Generative artificial intelligence (GAI) technologies are gaining traction in higher education, offering potential benefits such as personalized learning support and enhanced productivity. However, successful integration requires understanding the factors influencing students' adoption of these emerging tools. This study investigates the determinants shaping higher education students' adoption of GAI through the lens of the unified theory of acceptance and use of technology 2 framework. Data was collected from Pyatigorsk State University students and analyzed using structural equation modeling. The findings reveal habit (HB) as the most influential predictor of GAI adoption among students, followed by performance expectancy. Hedonic motivation, social influence (SI), and price value positively influenced behavioral intention (BI) to use these technologies. Surprisingly, facilitating conditions (FCs) exhibited a negative effect on BI, suggesting potential gaps in support systems. The study identifies no significant gender differences in the underlying factors driving adoption. Based on the results, recommendations are provided to foster HB formation, communicate benefits, enhance hedonic appeal, leverage SI, address price concerns, and strengthen FCs. Potential limitations include the cross-sectional nature of the data, geographic constraints, reliance on self-reported measures, and the lack of consideration for individual differences as moderators. This research contributes to the growing body of knowledge on GAI adoption in educational contexts, offering insights to guide higher education institutions in responsibly integrating these innovative tools while addressing student needs and promoting improved learning outcomes.