Effective scene representation is critical for the visual grounding ability of representations, yet existing methods for 3D Visual Grounding are often constrained. They either only focus on geometric and visual cues, or, like traditional 3D scene graphs, lack the multi-dimensional attributes needed for complex reasoning. To bridge this gap, we introduce the Diverse Semantic Map (DSM) framework, a novel scene representation framework that enriches robust geometric models with a spectrum of VLM-derived semantics, including appearance, physical properties, and affordances. The DSM is first constructed online by fusing multi-view observations within a temporal sliding window, creating a persistent and comprehensive world model. Building on this foundation, we propose DSM-Grounding, a new paradigm that shifts grounding from free-form VLM queries to a structured reasoning process over the semantic-rich map, markedly improving accuracy and interpretability. Extensive evaluations validate our approach's superiority. On the ScanRefer benchmark, DSM-Grounding achieves a state-of-the-art 59.06% overall accuracy of IoU@0.5, surpassing others by 10%. In semantic segmentation, our DSM attains a 67.93% F-mIoU, outperforming all baselines, including privileged ones. Furthermore, successful deployment on physical robots for complex navigation and grasping tasks confirms the framework's practical utility in real-world scenarios.