Lung registration in thoracic CT scans has received much attention in the medical imaging community. Possible applications range from follow-up analysis, motion correction for radiation therapy, monitoring of air flow and pulmonary function to lung elasticity analysis. In a clinical environment, runtime is always a critical issue, ruling out quite a few excellent registration approaches. In this paper, a highly efficient variational lung registration method based on minimizing the normalized gradient fields distance measure with curvature regularization is presented. The method ensures diffeomorphic deformations by an additional volume regularization. Supplemental user knowledge, like a segmentation of the lungs, may be incorporated as well. The accuracy of our method was evaluated on 40 test cases from clinical routine. In the EMPIRE10 lung registration challenge, our scheme ranks third, with respect to various validation criteria, out of 28 algorithms with an average landmark distance of 0.72 mm. The average runtime is about 1:50 min on a standard PC, making it by far the fastest approach of the top-ranking algorithms. Additionally, the ten publicly available DIR-Lab inhale-exhale scan pairs were registered to subvoxel accuracy at computation times of only 20 seconds. Our method thus combines very attractive runtimes with state-of-the-art accuracy in a unique way.