GeoShoot-GAN: Unsupervised Diffeomorphic Image Registration Using Geodesic Shooting and Generative Adversarial Networks

Abstract Deformable image registration is a fundamental step in medical image analysis. Diffeomorphic registration provides topology-preserving transformations which is an essential property for many clinical studies. Despite the theoretical strengths of geodesic shooting models, their high computational complexity and the absence of fully unsupervisedmethods have limited their widespread adoption. We propose GeoShoot-GAN, the first fully unsupervised, end-to-end framework for diffeomorphic registration via geodesic shooting. Our approach is based on adversarial learning, that allows the inference of complex deformable models without requiring the guidance ofground-truth deformations. We further extend the method to the stationary velocity field parameterization, providing a flexible framework that unifies geodesic andstationary variants. To stabilize adversarial training, we introduce tailored loss designs and careful optimization strategies that balance the relativedifficulty between generator and discriminator tasks. This design ensures that the generator produces smooth velocity fields while the discriminatorenforces plausibility on the image disimilarity after registration, driving the system toward realistic topology-preserving deformations. Experiments on two independent brain MRI datasets (NIREP and OASIS) demonstrate that GeoShoot-GAN achieves accurate diffeomorphic transformationsthrough efficient inference.The method performs competitively with state-of-the-art optimization- and learning- based methods, while preserving geodesic guarantees.Moreover, GeoShoot-GAN exhibits strong generalization across datasets, underscoring both its robustness and practical applicability. These results demonstrate the potential of adversarial learning as a powerful driver for unsupervised diffeomorphic registration, opening newopportunities for large-scale studies in Computational Anatomy and time-sensitive clinical applications, in contrast with diffusion modelsthat, while promissing, are still far from being computationally viable for this kind of studies.