Learning natural body motion remains challenging due to the strong coupling between spatial geometry and temporal dynamics. Embedding motion in phase manifolds, latent spaces that capture local periodicity, has proven effective for motion prediction; however, existing approaches lack scalability and remain confined to specific settings. We introduce FunPhase, a functional periodic autoencoder that learns a phase manifold for motion and replaces discrete temporal decoding with a function-space formulation, enabling smooth trajectories that can be sampled at arbitrary temporal resolutions. FunPhase supports downstream tasks such as super-resolution and partial-body motion completion, generalizes across skeletons and datasets, and unifies motion prediction and generation within a single interpretable manifold. Our model achieves substantially lower reconstruction error than prior periodic autoencoder baselines while enabling a broader range of applications and performing on par with state-of-the-art motion generation methods.