TRIDENT is a novel framework for domain generalization that eliminates the reliance on domain-specific text prompts and costly diffusion model fine-tuning. Instead, it leverages the linear structure of CLIP embeddings by decomposing them into domain, class, and attribute components. Through controlled reassembly of these components, TRIDENT generates semantically valid and structurally coherent synthetic samples across unseen domains. This lightweight embedding-space manipulation enables diverse and efficient data augmentation with minimal computational overhead. Extensive experiments on standard DG benchmarks such as PACS, VLCS, and OfficeHome demonstrate that TRIDENT achieves competitive or superior performance compared to existing approaches, while qualitative analyses highlight the effectiveness of the proposed decomposition strategy.