When multimode optical fibers are perturbed, the data that is transmitted through them is scrambled. This presents a major difficulty for many possible applications, such as multimode fiber based telecommunication and endoscopy. To overcome this challenge, a deep learning approach that generalizes over mechanical perturbations is presented. Using this approach, successful reconstruction of the input images from intensity-only measurements of speckle patterns at the output of a 1.5 m-long randomly perturbed multimode fiber is demonstrated. The model's success is explained by hidden correlations in the speckle of random fiber conformations.