Generative Artificial Intelligence (GenAI) is changing how knowledge is shared and used across many fields. Its use in research offers benefits but also raises perceptions of risk, value, and engagement that influence adoption. This study examines the factors influencing the adoption of GenAI among higher education research students by applying Partial Least Squares Structural Equation Modeling (PLS-SEM) and Importance–Performance Map Analysis (IPMA) to the identified latent factors, addressing gaps in the literature through a proposed model. Grounded in the Technology Acceptance Model (TAM), the study tests eleven hypothesized paths to examine how perceived risk, perceived value, perceived usefulness, and perceived ease of use influence user engagement and behavioral intention, with use behavior as the most endogenous variable. A total of 959 valid responses were collected from college students in Central Visayas, Philippines, enrolled in research courses who used GenAI to assist in preparing their manuscripts. PLS-SEM results showed that higher perceived value is associated with greater usefulness and easier use, which, in turn, enhances engagement with GenAI. IPMA results show that behavioral intention is the primary priority, given its greater importance than performance, while perceived value and engagement are secondary priorities. The hypothesis on perceived risk was not supported, and it is the least important factor, suggesting adoption should focus on value, intention, usability, and engagement.