The Sun is observed in unprecedented detail, enabling studies of its activity on very small spatiotemporal scales. However, the large volume of data collected by our telescopes cannot be fully analyzed with conventional methods. Popular machine learning methods identify general trends from observations, but tend to overlook unusual events due to their low frequency of occurrence. We study the applicability of unsupervised probabilistic methods to efficiently identify rare events in multidimensional solar observations and optimize our computational resources to the study of these extreme phenomena. We introduce Inspectorch, an open-source framework that utilizes flow-based models: flexible density estimators capable of learning the multidimensional distribution of solar observations. Once optimized, it assigns a probability to each sample, allowing us to identify unusual events. We apply this approach by applying it to observations from the Hinode Spectro-Polarimeter, the Interface Region Imaging Spectrograph, the Microlensed Hyperspectral Imager at Swedish 1-m Solar Telescope, the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory and the Extreme Ultraviolet Imager on board Solar Orbiter. We find that the algorithm assigns consistently lower probabilities to spectra that exhibit unusual features. For example, it identifies profiles with very strong Doppler shifts, uncommon broadening, and temporal dynamics associated with small-scale reconnection events, among others. As a result, Inspectorch demonstrates that density estimation using flow-based models offers a powerful approach to identifying rare events in large solar datasets. The resulting probabilistic anomaly scores allow computational resources to be focused on the most informative and physically relevant events. We make our Python package publicly available at https://github.com/cdiazbas/inspectorch.