Existing fusion methods are tailored for high-quality images but struggle with degraded images captured under harsh circumstances, thus limiting the practical potential of image fusion. This work presents a \textbf{D}egradation and \textbf{S}emantic \textbf{P}rior dual-guided framework for degraded image \textbf{Fusion} (\textbf{DSPFusion}), utilizing degradation priors and high-quality scene semantic priors restored via diffusion models to guide both information recovery and fusion in a unified model. In specific, it first individually extracts modality-specific degradation priors, while jointly capturing comprehensive low-quality semantic priors. Subsequently, a diffusion model is developed to iteratively restore high-quality semantic priors in a compact latent space, enabling our method to be over $20 \times$ faster than mainstream diffusion model-based image fusion schemes. Finally, the degradation priors and high-quality semantic priors are employed to guide information enhancement and aggregation via the dual-prior guidance and prior-guided fusion modules. Extensive experiments demonstrate that DSPFusion mitigates most typical degradations while integrating complementary context with minimal computational cost, greatly broadening the application scope of image fusion.