Generating effective query suggestions in conversational search requires aligning model outputs with user click preferences. However, directly optimizing for these preferences is difficult because click signals are sparse and inherently noisy. To address this, we propose Generative Query Suggestion (GQS), a generative framework that leverages click modeling to denoise implicit feedback and enables reliable preference optimization for improving real-world user engagement.GQS consists of three key components: (1) a Multi-Source CTR Modeling module that captures diverse contextual signals to estimate fine-grained click-through rates, thereby constructing more reliable user click-preference pairs; (2) a Diversity-Aware Preference Alignment strategy using CTR-weighted Direct Preference Optimization (DPO), which balances relevance and semantic diversity; and (3) a CTR-Calibrated Iterative Optimization process that jointly refines both the CTR model and the query suggestion model across training rounds, enabling effective data reuse.Experiments on two real-world tasks demonstrate that GQS outperforms strong baselines in CTR, relevance, and diversity.