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Longitudinal studies, where a series of images from the same set of individuals are acquired at different time-points, represent a popular technique for studying and characterizing temporal dynamics in biomedical applications. The classical approach for longitudinal comparison involves normalizing for nuisance variations, such as image orientation or contrast differences, via pre-processing. Statistical analysis is, in turn, conducted to detect changes of interest, either at the individual or population level. This classical approach can suffer from pre-processing issues and limitations of the statistical modeling. For example, normalizing for nuisance variation might be hard in settings where there are a lot of idiosyncratic changes. In this paper, we present a simple machine learning-based approach that can alleviate these issues. In our approach, we train a deep learning model (called PaIRNet, for Pairwise Image Ranking Network) to compare pairs of longitudinal images, with or without supervision. In the self-supervised setup, for instance, the model is trained to temporally order the images, which requires learning to recognize time-irreversible changes. Our results from four datasets demonstrate that PaIRNet can be very effective in localizing and quantifying meaningful longitudinal changes while discounting nuisance variation. Our code is available at \url{https://github.com/heejong-kim/learning-to-compare-longitudinal-images}
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