In zero-shot skeleton-based action recognition (ZSAR), aligning skeleton features with the text features of action labels is essential for accurately predicting unseen actions. ZSAR faces a fundamental challenge in bridging the modality gap between the two-kind features, which severely limits generalization to unseen actions. Previous methods focus on direct alignment between skeleton and text latent spaces, but the modality gaps between these spaces hinder robust generalization learning. Motivated by the success of diffusion models in multi-modal alignment (e.g., text-to-image, text-to-video), we firstly present a diffusion-based skeleton-text alignment framework for ZSAR. Our approach, Triplet Diffusion for Skeleton-Text Matching (TDSM), focuses on cross-alignment power of diffusion models rather than their generative capability. Specifically, TDSM aligns skeleton features with text prompts by incorporating text features into the reverse diffusion process, where skeleton features are denoised under text guidance, forming a unified skeleton-text latent space for robust matching. To enhance discriminative power, we introduce a triplet diffusion (TD) loss that encourages our TDSM to correct skeleton-text matches while pushing them apart for different action classes. Our TDSM significantly outperforms very recent state-of-the-art methods with significantly large margins of 2.36\%-point to 13.05\%-point, demonstrating superior accuracy and scalability in zero-shot settings through effective skeleton-text matching.