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

arXiv: https://arxiv.org/abs/2512.09423 · HTML: https://mlsanity.com/paper/2512.09423/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Executing your Commands via Motion Diffusion in Latent Space](https://mlsanity.com/paper/2212.04048/) (2022)
- [MotionGPT: Human Motion as a Foreign Language](https://mlsanity.com/paper/2306.14795/) (2023)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [Human Motion Generation: A Survey](https://mlsanity.com/paper/2307.10894/) (2023)
- [A Neural Temporal Model for Human Motion Prediction](https://mlsanity.com/paper/1809.03036/) (2018)
- [Real-Time Style Modelling of Human Locomotion via Feature-Wise Transformations and Local Motion Phases](https://mlsanity.com/paper/2201.04439/) (2022)
- [Go to Zero: Towards Zero-shot Motion Generation with Million-scale Data](https://mlsanity.com/paper/2507.07095/) (2025)
- [Single Motion Diffusion](https://mlsanity.com/paper/2302.05905/) (2023)
- [Taming Diffusion Probabilistic Models for Character Control](https://mlsanity.com/paper/2404.15121/) (2024)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [AnyTop: Character Animation Diffusion with Any Topology](https://mlsanity.com/paper/2502.17327/) (2025)
- [Continuous-Time Functional Diffusion Processes](https://mlsanity.com/paper/2303.00800/) (2023)
- [Spatio-temporal Manifold Learning for Human Motions via Long-horizon Modeling](https://mlsanity.com/paper/1908.07214/) (2019)
- [Absolute Coordinates Make Motion Generation Easy](https://mlsanity.com/paper/2505.19377/) (2025)
- [Motion In-Betweening with Phase Manifolds](https://mlsanity.com/paper/2308.12751/) (2023)
- [Scaling Large Motion Models with Million-Level Human Motions](https://mlsanity.com/paper/2410.03311/) (2024)
- [FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling](https://mlsanity.com/paper/2506.07902/) (2025)
- [DiffusionPhase: Motion Diffusion in Frequency Domain](https://mlsanity.com/paper/2312.04036/) (2023)
- [WalkTheDog: Cross-Morphology Motion Alignment via Phase Manifolds](https://mlsanity.com/paper/2407.18946/) (2024)
- [Motion Generation: A Survey of Generative Approaches and Benchmarks](https://mlsanity.com/paper/2507.05419/) (2025)
- [Deep Compositional Phase Diffusion for Long Motion Sequence Generation](https://mlsanity.com/paper/2510.14427/) (2025)
- [UniMoGen: Universal Motion Generation](https://mlsanity.com/paper/2505.21837/) (2025)
- [Scalable Group Choreography via Variational Phase Manifold Learning](https://mlsanity.com/paper/2407.18839/) (2024)

## Abstract (arXiv)

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 are tied to fixed skeletons and narrow motion distributions, limiting their applicability across diverse 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 unifies motion prediction and generation within a single interpretable phase manifold, enabling motion generation via latent diffusion, generalizes across skeletons and datasets, and supports downstream tasks such as motion super-resolution and partial-body completion. Our model achieves substantially lower reconstruction error than prior periodic autoencoder baselines, achieving uniform improvements of at least 45% across all metrics, while enabling a broader range of applications and performing on par with state-of-the-art motion generation methods.