We present a new approach for video-driven animation of high-quality neural 3D head models, addressing the challenge of person-independent animation from video input. Typically, high-quality generative models are learned for specific individuals from multi-view video footage, resulting in person-specific latent representations that drive the generation process. In order to achieve person-independent animation from video input, we introduce an LSTM-based animation network capable of translating person-independent expression features into personalized animation parameters of person-specific 3D head models. Our approach combines the advantages of personalized head models (high quality and realism) with the convenience of video-driven animation employing multi-person facial performance capture. We demonstrate the effectiveness of our approach on synthesized animations with high quality based on different source videos as well as an ablation study.