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Non-visual imaging sensors are widely used in the industry for different purposes. Those sensors are more expensive than visual (RGB) sensors, and usually produce images with lower resolution. To this end, Cross-Modality Super-Resolution methods were introduced, where an RGB image of a high-resolution assists in increasing the resolution of the low-resolution modality. However, fusing images from different modalities is not a trivial task; the output must be artifact-free and remain loyal to the characteristics of the target modality. Moreover, the input images are never perfectly aligned, which results in further artifacts during the fusion process. We present CMSR, a deep network for Cross-Modality Super-Resolution, which unlike previous methods, is designed to deal with weakly aligned images. The network is trained on the two input images only, learns their internal statistics and correlations, and applies them to up-sample the target modality. CMSR contains an internal transformer that is trained on-the-fly together with the up-sampling process itself, without explicit supervision. We show that CMSR succeeds to increase the resolution of the input image, gaining valuable information from its RGB counterpart, yet in a conservative way, without introducing artifacts or irrelevant details.