Deformable templates are essential to large-scale medical image registration, segmentation, and population analysis. Current conventional and deep network-based methods for template construction use only regularized registration objectives and often yield templates with blurry and/or anatomically implausible appearance, confounding downstream biomedical interpretation. We reformulate deformable registration and conditional template estimation as an adversarial game wherein we encourage realism in the moved templates with a generative adversarial registration framework conditioned on flexible image covariates. The resulting templates exhibit significant gain in specificity to attributes such as age and disease, better fit underlying group-wise spatiotemporal trends, and achieve improved sharpness and centrality. These improvements enable more accurate population modeling with diverse covariates for standardized downstream analyses and easier anatomical delineation for structures of interest.