Multimodal groupwise registration has been of growing interest to the image processing community due to developments in scanner technologies (e.g. multiparametric MRI, DCE-CT or PET-MR) that increased both the number of modalities and number of images under consideration. In this work a novel methodology is presented for multimodal groupwise registration that is based on Laplacian eigenmaps, a nonlinear dimensionality reduction technique. Compared to recently proposed dissimilarity metrics based on principal component analysis, the proposed metric should enable a better capture of the intensity relationships between different images in the group. The metric is constructed to be the second smallest eigenvalue from the eigenvector problem defined in Laplacian eigenmaps. The method was validated in three distinct experiments: a non-linear synthetic registration experiment, the registration of quantitative MRI data of the carotid artery, and the registration of multimodal data of the brain (RIRE). The results show increased accuracy and robustness compared to other state-of-the-art groupwise registration methodologies.