Inspired by the power of Diffusion Models (DM) verified in various fields, some pioneering works have started to explore DM in recommendation. However, these prevailing endeavors commonly implement diffusion on item indices, leading to the increasing time complexity, the lack of transferability, and the inability to fully harness item semantic information. To tackle these challenges, we propose SeeDRec, a sememe-based diffusion framework for sequential recommendation (SR). Specifically, inspired by the notion of sememe in NLP, SeeDRec first defines a similar concept of recommendation sememe to represent the minimal interest unit and upgrades the specific diffusion objective from the item level to the sememe level. With the Sememe-to-Interest Diffusion Model (S2IDM), SeeDRec can accurately capture the user's diffused interest distribution learned from both local interest evolution and global interest generalization while maintaining low computational costs. Subsequently, an Interest-aware Prompt-enhanced (IPE) strategy is proposed to better guide each user's sequential behavior modeling via the learned user interest distribution. Extensive experiments on nine SR datasets and four cross-domain SR datasets verify its effectiveness and universality. The code is available in https://github.com/hulkima/SeeDRec.