The aim of this study was to computationally model, in an unsupervised manner, a manifold of symmetry variations in normal brains, such that the learned manifold can be used to segment brain tumors from magnetic resonance (MR) images that fail to exhibit symmetry. An unsupervised brain tumor segmentation method, named as symmetric driven generative adversarial network (SD-GAN), was proposed. SD-GAN model was trained to learn a non-linear mapping between the left and right brain images, and thus being able to present the variability of the (symmetry) normal brains. The trained SD-GAN was then used to reconstruct normal brains and to segment brain tumors based on higher reconstruction errors arising from their being unsymmetrical. SD-GAN was evaluated on two public benchmark datasets (Multi-modal Brain Tumor Image Segmentation (BRATS) 2012 and 2018). SD-GAN provided best performance with tumor segmentation accuracy superior to the state-of-the-art unsupervised segmentation methods and performed comparably (less than 3% lower in Dice score) to the supervised U-Net (the most widely used supervised method for medical images). This study demonstrated that symmetric features presenting variations (i.e., inherent anatomical variations) can be modelled using unannotated normal MR images and thus be used in segmenting tumors.