Objective. Online adaptive radiotherapy aims to fully leverage the advantages of highly conformal therapy by reducing anatomical and set-up uncertainty, thereby alleviating the need for robust treatments. This requires extensive automation, among which is the use of deformable image registration (DIR) for contour propagation and dose accumulation. However, inconsistencies in DIR solutions between different algorithms have caused distrust, hampering its direct clinical use. This work aims to enable the clinical use of DIR by developing deep learning methods to predict DIR uncertainty and propagating it into clinically usable metrics. Approach. Supervised and unsupervised neural networks were trained to predict the Gaussian uncertainty of a given deformable vector field (DVF). Since both methods rely on different assumptions, their predictions differ and were further merged into a combined model. The resulting normally distributed DVFs can be directly sampled to propagate the uncertainty into contour and accumulated dose uncertainty. Main results. The unsupervised and combined models can accurately predict the uncertainty in the manually annotated landmarks on the DIRLAB dataset. Furthermore, for 5 patients with lung cancer, the propagation of the predicted DVF uncertainty into contour uncertainty yielded for both methods an expected calibration error of less than 3%. Additionally, the probabilisticly accumulated dose volume histograms (DVH) encompass well the accumulated proton therapy doses using 5 different DIR algorithms. It was additionally shown that the unsupervised model can be used for different DIR algorithms without the need for retraining. Significance. Our work presents first-of-a-kind deep learning methods to predict the uncertainty of the DIR process. The methods are fast, yield high-quality uncertainty estimates and are useable for different algorithms and applications. This allows clinics to use DIR uncertainty in their workflows without the need to change their DIR implementation.