Dexterous grasp synthesis must jointly satisfy functional intent and physical feasibility, yet existing pipelines often decouple semantic grounding from refinement, yielding unstable or non-functional contacts under object and pose variations. This challenge is exacerbated by the high dimensionality and kinematic diversity of multi-fingered hands, which makes many methods rely on large, hardware-specific grasp datasets collected in simulation or through costly real-world trials. We propose a data-efficient framework that bypasses robot grasp data collection by exploiting object-centric semantic priors in pretrained generative diffusion models. Temporally aligned and fine-grained grasp affordances are extracted from raw human video demonstrations and fused with 3D scene geometry from depth images to infer semantically grounded contact targets. We further incorporate these affordance regions into the grasp refinement objective, explicitly guiding each fingertip toward its predicted region during optimization. The resulting system produces stable, human-intuitive multi-contact grasps across common objects and tools, while exhibiting strong generalization to previously unseen object instances within a category, pose variations, and multiple hand embodiments.This work (i) introduces a semantic affordance extraction pipeline leveraging vision--language generative priors for dexterous grasping, (ii) demonstrates cross-hand generalization without constructing hardware-specific grasp datasets, and (iii) establishes that a single depth modality suffices for high-performance grasp synthesis when coupled with foundation-model semantics. Our results highlight a path toward scalable, hardware-agnostic dexterous manipulation driven by human demonstrations and pretrained generative models.