Semantic image compression aims to reduce the amount of data transmitted by leveraging high-level semantic information for image representation and reconstruction. Considering that objects in an image vary in semantic importance, we propose a semantic-aware image compression framework that employs a diffusion model as the decoder to reconstruct visually pleasing images. The latent code generated by an autoencoder is used as a conditional input for the reverse diffusion process, where semantic importance is explicitly incorporated. To enhance the reconstruction of fine-grained details, we design a novel noise scheduling function tailored for conditional diffusion generation. Additionally, a two-stage reverse diffusion process with semantic-aware scheduling is proposed: The first stage focuses on improving the reconstruction quality of semantically critical regions, while the second stage refines the remaining areas. Experimental results demonstrate that the proposed method achieves higher perceptual quality compared to baseline approaches, along with improved pixel fidelity and semantic fidelity for semantically significant objects.