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Despite the effectiveness of supervised skeleton-based methods, their reliance on exhaustive annotation limits generalization to novel actions. Zero-Shot Skeleton Action Recognition (ZSAR) emerges as a promising paradigm, yet it faces challenges due to the spectral bias of diffusion models, which oversmooth high-frequency dynamics. Here, we propose Frequency-Aware Diffusion for Skeleton-Text Matching (FDSM), integrating a Semantic-Guided Spectral Residual Module, a Timestep-Adaptive Spectral Loss, and Curriculum-based Semantic Abstraction to address these challenges. Our approach effectively recovers fine-grained motion details, achieving state-of-the-art performance on NTU RGB+D, PKU-MMD, and Kinetics-skeleton datasets. Code has been made available at https://github.com/yuzhi535/FDSM. 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