FunPhase: A Periodic Functional Autoencoder for Motion Generation via Phase Manifolds

TL;DR

FunPhase introduces a functional periodic autoencoder that learns a phase manifold for motion and reconstructs motion as a continuous spatio-temporal function, enabling smooth sampling at arbitrary temporal resolutions and skeleton-agnostic generation. By integrating a phase decomposition and a diffusion model in function space, the approach unifies motion prediction and generation while achieving state-of-the-art reconstruction and competitive generation quality across diverse datasets. The method demonstrates strong capabilities in motion super-resolution, partial-body completion, and controllable generation, supported by extensive ablations and comparisons to existing phase-based and diffusion-based baselines. This work highlights the advantage of combining phase-aware priors with functional representations to enhance stability, realism, and generalization in animated motion synthesis.

Abstract

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.

Figures (7)

• Figure 1: FunPhase is a functional periodic autoencoder that learns a phase-structured manifold for motion, enabling smooth, continuous spatio-temporal reconstruction, and skeleton-agnostic motion prediction and generation.
• Figure 2: Overview of the Periodic Function Autoencoder (FunPhase) architecture. The figure illustrates the separated processing of joint rotations and root positions through Perceiver-based encoder–decoder modules. The latent space is decomposed by a Fast Fourier Transform (FFT) layer in its periodic components (Phase shift, Amplitude, Frequency, Bias) to achieve an even more compact representation and enforce periodicity. The latent space is then reconstructed with the inverse FFT, and the functions are evaluated at the coordinates given as input to the decoder.
• Figure 3: Phase Manifold. The plots show the phase manifolds obtained with DeepPhase and FunPhase, alongside the original motion features. All encoded sequences correspond to a dog-running motion.
• Figure 4: FunPhase super-resolution. Given a sparse set of keyframes, FunPhase reconstructs the full continuous motion while preserving physical plausibility.
• Figure 5: Diffusion examples on 100STYLE. On the left we show and example of generation from a sparse set of key frames (in green). On the right we show an example of body completion of the right leg (in pink).