We present a Gauss-Newton-Krylov solver for large deformation diffeomorphic image registration. We extend the publicly available CLAIRE library to multi-node multi-graphics processing unit (GPUs) systems and introduce novel algorithmic modifications that significantly improve performance. Our contributions comprise ($i$) a new preconditioner for the reduced-space Gauss-Newton Hessian system, ($ii$) a highly-optimized multi-node multi-GPU implementation exploiting device direct communication for the main computational kernels (interpolation, high-order finite difference operators and Fast-Fourier-Transform), and ($iii$) a comparison with state-of-the-art CPU and GPU implementations. We solve a $256^3$-resolution image registration problem in five seconds on a single NVIDIA Tesla V100, with a performance speedup of 70% compared to the state-of-the-art. In our largest run, we register $2048^3$ resolution images (25 B unknowns; approximately 152$times$ larger than the largest problem solved in state-of-the-art GPU implementations) on 64 nodes with 256 GPUs on TACCs Longhorn system.
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