# Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion

arXiv: https://arxiv.org/abs/2610.18871 · HTML: https://mlsanity.com/paper/2610.18871/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 116 of its 158 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 30 of 116)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
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- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [TAPIR: Tracking Any Point with per-frame Initialization and temporal Refinement](https://mlsanity.com/paper/2306.08637/) (2023)
- [PointOdyssey: A Large-Scale Synthetic Dataset for Long-Term Point Tracking](https://mlsanity.com/paper/2307.15055/) (2023)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [TAP-Vid: A Benchmark for Tracking Any Point in a Video](https://mlsanity.com/paper/2211.03726/) (2022)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [TripoSR: Fast 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/2403.02151/) (2024)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [Particle Video Revisited: Tracking Through Occlusions Using Point Trajectories](https://mlsanity.com/paper/2204.04153/) (2022)
- [Robust Dynamic Radiance Fields](https://mlsanity.com/paper/2301.02239/) (2023)
- [Tracking Everything Everywhere All at Once](https://mlsanity.com/paper/2306.05422/) (2023)
- [RH20T: A Comprehensive Robotic Dataset for Learning Diverse Skills in One-Shot](https://mlsanity.com/paper/2307.00595/) (2023)
- [SpatialTracker: Tracking Any 2D Pixels in 3D Space](https://mlsanity.com/paper/2404.04319/) (2024)
- [Data Determines Distributional Robustness in Contrastive Language Image Pre-training (CLIP)](https://mlsanity.com/paper/2205.01397/) (2022)

## Abstract (arXiv)

Sparse-to-dense motion completion recovers dense mesh motion from sparse vertex displacements. Residual priors trained on one geometry family frequently fail to beat parameter-free harmonic extension off-family. Moreover, cross-family training meets a scaling barrier: residual amplitude varies by more than an order of magnitude across geometry families and collapses as observations become denser. Since this scale depends on unknown target motion, it cannot be measured directly at test time. We decouple residual structure from physical scale by learning a dimensionless prior, estimating amplitude from observables and a lightweight correction fitted only on training sources. Our unified model surpasses harmonic extension across all evaluated families, including unseen cloth and legged bodies, without skeletons, registration, or cross-mesh correspondence. The same prior applies without retraining to point-tracked animal video and a robot grasping a soft body. Project page: https://su-terry.github.io/cepheid-website/