Image normalization is a critical step in medical imaging. This step is often done on a per-dataset basis, preventing current segmentation algorithms from the full potential of exploiting jointly normalized information across multiple datasets. To solve this problem, we propose an adversarial normalization approach for image segmentation which learns common normalizing functions across multiple datasets while retaining image realism. The adversarial training provides an optimal normalizer that improves both the segmentation accuracy and the discrimination of unrealistic normalizing functions. Our contribution therefore leverages common imaging information from multiple domains. The optimality of our common normalizer is evaluated by combining brain images from both infants and adults. Results on the challenging iSEG and MRBrainS datasets reveal the potential of our adversarial normalization approach for segmentation, with Dice improvements of up to 59.6% over the baseline.