Existing infrared-visible image fusion methods are mainly tailored for high-quality source images. Although recent studies have begun to explore degradation-aware fusion, most existing methods still focus on specific degradation types, while unified frameworks that aim to handle diverse degradations often depend on auxiliary textual prompts, which limits their practicality in automatic fusion scenarios. This work presents a Degradation and Semantic Prior dual-guided framework for degraded image Fusion (DSPFusion), which jointly performs degradation-aware restoration and complementary information aggregation in a unified architecture without relying on auxiliary prompts. Specifically, it first extracts modality-specific degradation priors from degraded infrared and visible images, while capturing compact semantic embeddings from paired source images as low-quality semantic priors to encode global scene context. Then, a semantic prior diffusion model is devised to restore high-quality scene semantic priors in a compact latent space, providing global scene guidance with low computational overhead and enabling over $30\times $ inference speedup compared with mainstream diffusion model-based image fusion schemes, such as DDFM. Guided by the restored semantic priors and degradation priors, the enhancement and fusion network adaptively suppresses degradations and aggregates complementary information. Extensive experiments under both degraded and normal scenarios demonstrate that DSPFusion effectively handles representative degradations, preserves complementary information, and achieves competitive performance with low computational cost, thereby broadening the practical application scope of image fusion. The source code is publicly available at https://github.com/Linfeng-Tang/DSPFusion.