We introduce PulseSearch, a GenAI-based approach for generating query suggestions in a music search platform. Designed to anticipate users’ intent during a search session, PulseSearch combines long- and short-term user signals by conditioning generation on both recent user queries and pre-generated listener profiles. To further enhance contextual relevance, it generates suggestions tailored to different times of the day. We conduct both online and offline evaluations, showing that PulseSearch consistently improves suggestion quality over dense retrieval baselines across dimensions such as personalization, diversity, and freshness. A demo of our results is available at the provided URL.