Xincan Feng, Noriki Nishida, Yusuke Sakai et al.
Prior work reports conflicting results on query diversity in synthetic data generation for dense retrieval. We identify this conflict and design Q-D metrics to quantify diversity's impact, making the problem measurable. Through experiments on 4 benchmark types (31 datasets), we find query diversity especially benefits multi-hop retrieval. Deep analysis on multi-hop data reveals that diversity benefit correlates strongly with query complexity ($r$$\geq$0.95, $p$$<$0.05 in 12/14 conditions), measured by content words (CW). We formalize this as the Complexity-Diversity Principle (CDP): query complexity determines optimal diversity. CDP provides actionable thresholds (CW$>$10: use diversity; CW$<$7: avoid it). Guided by CDP, we propose zero-shot multi-query synthesis for multi-hop tasks, achieving state-of-the-art performance.