Context: Software engineering (SE) researchers increasingly study Generative AI (GenAI) while also incorporating it into their own research practices. Despite rapid adoption, there is limited empirical evidence on how GenAI is used in SE research and its implications for research practices and governance. Aims: We conduct a large-scale survey of 457 SE researchers publishing in top venues between 2023 and 2025. Method: Using quantitative and qualitative analyses, we examine who uses GenAI and why, where it is used across research activities, and how researchers perceive its benefits, opportunities, challenges, risks, and governance. Results: GenAI use is widespread, with many researchers reporting pressure to adopt and align their work with it. Usage is concentrated in writing and early-stage activities, while methodological and analytical tasks remain largely human-driven. Although productivity gains are widely perceived, concerns about trust, correctness, and regulatory uncertainty persist. Researchers highlight risks such as inaccuracies and bias, emphasize mitigation through human oversight and verification, and call for clearer governance, including guidance on responsible use and peer review. Conclusion: We provide a fine-grained, SE-specific characterization of GenAI use across research activities, along with taxonomies of GenAI use cases for research and peer review, opportunities, risks, mitigation strategies, and governance needs. These findings establish an empirical baseline for the responsible integration of GenAI into academic practice.