Glioma progression is monitored by routine MR scanning, enabling tumor growth evaluation with respect to earlier time-points. This growth may present both as a mass effect and as an extension of abnormalities into previously healthy tissue. To accurately quantify tumor growth and tumor-induced deformations, longitudinal intrasubject image registration is often used. However, such registration in cases with large deformations and tissue change is highly challenging. Longitudinal image registration may benefit from groupwise strategies in which multiple images are concurrently aligned. This avoids introducing bias towards an a priori-selected reference image. However, existing learning-based methods for image registration mostly concern pair-wise approaches. Moreover, the few proposed learning-based methods for groupwise registration are designed for the analysis of images without pathologies and are prone to fail to register glioma images. To bridge this gap, we present a learning-based method for the non-linear registration of longitudinal glioma images. We adapt an existing learning-based groupwise method to handle tumor infiltration by means of cost-function masking. The proposed method is able to register glioma images despite the presence of non-correspondences across the time-points by focusing on the normal-appearing tissue similarity. We train the framework both in one resolution and with a multi-stage strategy exploring multiple resolutions. We evaluate on a dataset from the Glioma Longitudinal AnalySiS consortium and compare it to conventional groupwise registration methods. We achieve comparable Dice coefficients, with higher SSIM and more detailed registrations. These evaluation metrics are further improved when trained as a multi-stage method. The proposed framework preserves the diffeomorphic conditions and the geometric centrality of the deformation fields, while significantly reducing the runtime to under a minute. The proposed methods may serve as an alternative to conventional toolboxes to provide further insight into glioma growth.