Face synthesis, including face aging, in particular, has been one of the major topics that witnessed a substantial improvement in image fidelity by using generative adversarial networks (GANs). Most existing face aging approaches divide the dataset into several age groups and leverage group-based training strategies, which lacks the ability to provide fine-controlled continuous aging synthesis in nature. In this work, we propose a unified network structure that embeds a linear age estimator into a GAN-based model, where the embedded age estimator is trained jointly with the encoder and decoder to estimate the age of a face image and provide a personalized target age embedding for age progression/regression. The personalized target age embedding is synthesized by incorporating both personalized residual age embedding of the current age and exemplar-face aging basis of the target age, where all preceding aging bases are derived from the learned weights of the linear age estimator. This formulation brings the unified perspective of estimating the age and generating personalized aged face, where self-estimated age embeddings can be learned for every single age. The qualitative and quantitative evaluations on different datasets further demonstrate the significant improvement in the continuous face aging aspect over the state-of-the-art.