Dexterous grasping across diverse object scales requires contact modes ranging from two-finger pinches to bimanual grasps. Existing dexterous grasp synthesis methods reduce the high-dimensional optimization space with manually designed expected contacts and initialization heuristics, which struggle to balance synthesis success rate and diversity. We present HUGS (Human-prior-guided Unified Dexterous Grasp Synthesis), a human-prior-guided framework for unified dexterous grasp synthesis across modes and scales. Instead of directly retargeting human demonstrations, HUGS learns an object-conditioned human prior that captures human grasp preferences and guides downstream force-closure-aware optimization. The prior is trained on a compact self-collected human grasp dataset with 1.8K grasps over 304 objects, providing broad coverage of object scales and contact modes. During synthesis, HUGS adaptively proposes contact modes and wrist initializations, substantially improving the balance between contact-mode coverage and synthesis success rate over heuristic-based methods. With HUGS, we synthesize 3.2M robotic grasps over 157K scenes, spanning object half-diagonal lengths from 2 cm to 30 cm and modes from two-finger to bimanual grasps. Models trained on the synthesized dataset autonomously select appropriate contact modes in the real world, enabling grasping from screws to large boxes.

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