In image restoration (IR), leveraging semantic priors from segmentation models has been a common approach to improve performance. The recent segment anything model (SAM) has emerged as a powerful tool for extracting advanced semantic priors to enhance IR tasks. However, the computational cost of SAM is prohibitive for IR, compared to existing smaller IR models. The incorporation of SAM for extracting semantic priors considerably hampers the model inference efficiency. To address this issue, we propose a general framework to distill SAM's semantic knowledge to boost exiting IR models without interfering with their inference process. Specifically, our proposed framework consists of the semantic prior fusion (SPF) scheme and the semantic prior distillation (SPD) scheme. SPF fuses two kinds of information between the restored image predicted by the original IR model and the semantic mask predicted by SAM for the refined restored image. SPD leverages a self-distillation manner to distill the fused semantic priors to boost the performance of the original IR model. Additionally, we design a semantic-guided relation (SGR) loss for SPD, which ensures semantic feature representation space consistency to fully distill the priors. We demonstrate the effectiveness of our general framework across multiple IR models and tasks, including deraining, deblurring, and denoising.