Infrared and visible images of the same scene are fused to produce a fused image with richer information. However, most current image-fusion algorithms suffer from insufficient edge information retention, weak feature representation, and poor contrast, halos, and artifacts, and can only be applied to a single scene. To address these issues, we propose a novel infrared and visual image fusion algorithm based on a bilateral–least-squares hybrid filter (DBLSF) with the least-squares and bilateral filter hybrid model (BLF-LS). The proposed algorithm utilizes the residual network ResNet50 and the adaptive fusion strategy of the structure tensor to fuse the base and detail layers of the filter decomposition, respectively. Experiments on 32 sets of images from the TNO image-fusion dataset show that, although our fusion algorithm sacrifices overall time efficiency, the Combination 1 approach can better preserve image edge information and image integrity; reduce the loss of source image features; suppress artifacts and halos; and compare favorably with other algorithms in terms of structural similarity, feature similarity, multiscale structural similarity, root mean square error, peak signal-to-noise ratio, and correlation coefficient by at least 2.71%, 1.86%, 0.09%, 0.46%, 0.24%, and 0.07%; and the proposed Combination 2 can effectively improve the contrast and edge features of the fused image and enrich the image detail information, with an average improvement of 37.42%, 26.40%, and 26.60% in the three metrics of average gradient, edge intensity, and spatial frequency compared with other algorithms.