  Image fusion typically employs non-invertible neural networks to merge
multiple source images into a single fused image. However, for clinical
experts, solely relying on fused images may be insufficient for making
diagnostic decisions, as the fusion mechanism blends features from source
images, thereby making it difficult to interpret the underlying tumor
pathology. We introduce FusionINN, a novel decomposable image fusion framework,
capable of efficiently generating fused images and also decomposing them back
to the source images. FusionINN is designed to be bijective by including a
latent image alongside the fused image, while ensuring minimal transfer of
information from the source images to the latent representation. To the best of
our knowledge, we are the first to investigate the decomposability of fused
images, which is particularly crucial for life-sensitive applications such as
medical image fusion compared to other tasks like multi-focus or multi-exposure
image fusion. Our extensive experimentation validates FusionINN over existing
discriminative and generative fusion methods, both subjectively and
objectively. Moreover, compared to a recent denoising diffusion-based fusion
model, our approach offers faster and qualitatively better fusion results.
