The spatial resolution of a hyperspectral image (HSI) can be enhanced by utilizing a co-registered high-resolution multispectral image (MSI) via an image fusion algorithm. This is an active area of research with applications ranging from precision agriculture, to security issues, to mineral identification and mapping, etc. The nearest-neighbor diffusion (NNDiffuse) algorithm has seen tremendous success in being utilized as a pansharpening algorithm to fuse an MSI with a broadband high-resolution panchromatic image and is implemented in commercial software applications, such as ENVI (L3Harris). We extended NNDiffuse to the problem of hyprespectral–multispectral image fusion (HS + MS). Hyperspectral pansharpening is a special case of this: a single high-resolution broadband (panchromatic) image is fused with a low-resolution HSI. Deep-learning (DL)-based methods can achieve excellent results in the area of HS + MS data fusion, but DL algorithms are data hungry: they need extensive training data, require special computing architectures, are slower to implement, etc. NNDiffuse introduces much less spectral distortions compared to state-of-the-art methods, does not need any training data or expensive computing resources, and is significantly faster compared to DL-based approaches. We: (1) demonstrate the utility of NNDiffuse in low-resolution HSI–MSI sharpening; (2) test three deep learning-based image fusion algorithms and compare performance with NNDiffuse and other non-DL-based fusion algorithms using global/image-wide quality metrics; and (3) assess fusion performance using an application based approach: adaptive coherence estimator target detection. The proposed method is tested against several datasets of varying scene content and complexity, and we demonstrate that the NNDiffuse fusion method outperforms the other baseline methods when the application of target detection is considered.