We formulate the motor system of an interactive avatar as a generative motion model that can drive the body to move through 3D space in a perpetual, realistic, controllable, and responsive manner. Although human motion generation has been extensively studied, many existing methods lack the responsiveness and realism of real human movements. Inspired by recent advances in foundation models, we propose PRIMAL, which is learned with a two-stage paradigm. In the pretraining stage, the model learns body movements from a large number of sub-second motion segments, providing a generative foundation from which more complex motions are built. This training is fully unsupervised without annotations. Given a single-frame initial state during inference, the pretrained model not only generates unbounded, realistic, and controllable motion, but also enables the avatar to be responsive to induced impulses in real time. In the adaptation phase, we employ a novel ControlNet-like adaptor to fine-tune the base model efficiently, adapting it to new tasks such as few-shot personalized action generation and spatial target reaching. Evaluations show that our proposed method outperforms state-of-the-art baselines. We leverage the model to create a real-time character animation system in Unreal Engine that feels highly responsive and natural.