# Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Tracking

arXiv: https://arxiv.org/abs/2401.06614 · HTML: https://mlsanity.com/paper/2401.06614/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 56 of its 71 references that are in the map.
- First posted on arXiv 12 Jan 2024.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 56)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [MotionDiffuse: Text-Driven Human Motion Generation with Diffusion Model](https://mlsanity.com/paper/2208.15001/) (2022)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [MoFusion: A Framework for Denoising-Diffusion-based Motion Synthesis](https://mlsanity.com/paper/2212.04495/) (2022)

## Built on by (most cited first, 29 of 29)

- [PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation](https://mlsanity.com/paper/2509.20358/) (2025)
- [GAF: Gaussian Avatar Reconstruction from Monocular Videos via Multi-view Diffusion](https://mlsanity.com/paper/2412.10209/) (2024)
- [Gaussian Variation Field Diffusion for High-fidelity Video-to-4D Synthesis](https://mlsanity.com/paper/2507.23785/) (2025)
- [AnimateAnyMesh: A Feed-Forward 4D Foundation Model for Text-Driven Universal Mesh Animation](https://mlsanity.com/paper/2506.09982/) (2025)
- [LaGeM: A Large Geometry Model for 3D Representation Learning and Diffusion](https://mlsanity.com/paper/2410.01295/) (2024)
- [ActionMesh: Animated 3D Mesh Generation with Temporal 3D Diffusion](https://mlsanity.com/paper/2601.16148/) (2026)
- [Mesh4D: 4D Mesh Reconstruction and Tracking from Monocular Video](https://mlsanity.com/paper/2601.05251/) (2026)
- [DNF: Unconditional 4D Generation with Dictionary-based Neural Fields](https://mlsanity.com/paper/2412.05161/) (2024)
- [4D-Bench: Benchmarking Multi-modal Large Language Models for 4D Object Understanding](https://mlsanity.com/paper/2503.17827/) (2025)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [Representing 3D Shapes With 64 Latent Vectors for 3D Diffusion Models](https://mlsanity.com/paper/2503.08737/) (2025)
- [FreeOrbit4D: Training-Free Arbitrary Camera Redirection for Monocular Videos via Foreground-Complete 4D Reconstruction](https://mlsanity.com/paper/2601.18993/) (2026)
- [Advances in 4D Representation: Geometry, Motion, and Interaction](https://mlsanity.com/paper/2510.19255/) (2025)
- [AnimateAnyMesh++: A Flexible Feed-Forward Framework for High-Fidelity Text-Driven Mesh Animation](https://mlsanity.com/paper/2604.26917/) (2026)
- [TwoSquared: 4D Generation from 2D Image Pairs](https://mlsanity.com/paper/2504.12825/) (2025)
- [ViPS: Video-informed Pose Spaces for Auto-Rigged Meshes](https://mlsanity.com/paper/2604.17623/) (2026)
- [FOLIAGE: Towards Physical Intelligence World Models Via Unbounded Surface Evolution](https://mlsanity.com/paper/2506.03173/) (2025)
- [NF3DM: Combining Neural Fields and Deformation Models for 3D Non-Rigid Motion Reconstruction](https://mlsanity.com/paper/2412.08511/) (2024)
- [ERNet: Efficient Non-Rigid Registration Network for Point Sequences](https://mlsanity.com/paper/2510.15800/) (2025)
- [Inferring Compositional 4D Scenes without Ever Seeing One](https://mlsanity.com/paper/2512.05272/) (2025)
- [Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences](https://mlsanity.com/paper/2602.22212/) (2026)
- [Fast 4D Mesh Generation by Spatio-Temporal Attention Chains](https://mlsanity.com/paper/2605.19786/) (2026)
- [Breaking the Rigid Prior: Towards Articulated 3D Anomaly Detection](https://mlsanity.com/paper/2604.26868/) (2026)
- [Velox: Learning Representations of 4D Geometry and Appearance](https://mlsanity.com/paper/2605.04527/) (2026)
- [DynaTok: Token-Based 4D Reconstruction from Partial Point Clouds](https://mlsanity.com/paper/2606.12189/) (2026)
- [4Director: Controlling Video World Models with Rigid 3D Geometry](https://mlsanity.com/paper/2610.02160/) (2026)
- [Render to Reason: Novel-View Semantic Prediction Improves Spatial Understanding in VLMs](https://mlsanity.com/paper/2610.05417/) (2026)
- [Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion](https://mlsanity.com/paper/2610.18871/) (2026)

## Abstract (arXiv)

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations. More detailed information can be found at https://vveicao.github.io/projects/Motion2VecSets/.