In recent years, image fusion has been a research hotspot. However, it is still a big challenge to balance the problems of noiseless image fusion and noisy image fusion. In order to improve the weak performance and low robustness of existing image fusion algorithms in noisy images, an infrared and visible image fusion algorithm based on optimized low-rank matrix factorization with guided filtering is proposed. First, the minimized error reconstruction factorization is introduced into the low-rank matrix, which effectively enhances the optimization performance, and obtains the base image with good filtering performance. Then using the base image as the guide image, the source image is decomposed into the high-frequency layer containing detail information and noise, and the low-frequency layer containing energy information through guided filtering. According to the noise intensity, the sparse reconstruction error is adaptively obtained to fuse the high-frequency layers, and the weighted average strategy is utilized to fuse the low-frequency layers. Finally, the fusion image is obtained by reconstructing the pre-fused high-frequency layer and the pre-fused low-frequency layer. The comparative experiments show that the proposed algorithm not only has good performance for noise-free images, but more importantly, it can effectively deal with the fusion of noisy images.