Convolutional networks are successful, but have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks do not struggle with learning each possible orientation of each image feature separately. So far, they have been proposed for 2D and 3D data. Here we generalize them to 6D diffusion MRI data, ensuring joint equivariance under 3D roto-translations in image space and the matching rotations in q-space, as dictated by the image formation. We validate our method on multiple-sclerosis lesion segmentation. Our proposed neural networks yield better results and require less training data.