Robust generalization in robotic manipulation is crucial for robots to adapt flexibly to diverse environments. Existing methods usually improve generalization by scaling data and networks, but model tasks independently and overlook skill-level information. Observing that tasks within the same skill share similar motion patterns, we propose Skill-Aware Diffusion (SADiff), which explicitly incorporates skill-level information to improve generalization. SADiff learns skill-specific representations through a skill-aware encoding module with learnable skill tokens, and conditions a skill-constrained diffusion model to generate object-centric motion flow. A skill-retrieval transformation strategy further exploits skill-specific trajectory priors to refine the mapping from 2D motion flow to executable 3D actions. Furthermore, we introduce IsaacSkill, a high-fidelity dataset containing fundamental robotic skills for comprehensive evaluation and sim-to-real transfer. Experiments in simulation and real-world settings show that SADiff achieves good performance and generalization across various manipulation tasks. Dataset and videos are available at https://sites.google.com/view/sa-diff.

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