mlsanityData to 7 Oct 2026

Equivariant Flow Matching for Point Cloud Assembly

arXiv 2505.21539 ↗First posted 24 May 2025cs.CV cs.AIcited by 2

On the map: Diffusion models → 3D, point cloud and scene generation

Abstract (arXiv)

The goal of point cloud assembly is to reconstruct a complete 3D shape by aligning multiple point cloud pieces. This work presents a novel equivariant solver for assembly tasks based on flow matching models. We first theoretically show that the key to learning equivariant distributions via flow matching is to learn related vector fields. Based on this result, we propose an assembly model, called equivariant diffusion assembly (Eda), which learns related vector fields conditioned on the input pieces. We further construct an equivariant path for Eda, which guarantees high data efficiency of the training process. Our numerical results show that Eda is highly competitive on practical datasets, and it can even handle the challenging situation where the input pieces are non-overlapped.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models. Builds on 40 of its 53 references that are in the map. First posted on arXiv 24 May 2025.

Builds on

40 of 53 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly29 Feb
  2. 2023PCRDiffusion: Diffusion Probabilistic Models for Point Cloud Registration11 Dec
  3. 2023SE(3) Diffusion Model-based Point Cloud Registration for Robust 6D Object Pose Estimation26 Oct

Other references · 37

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2020Scaling Laws for Neural Language Modelscited by 6,411
  4. 2022Scalable Diffusion Models with Transformerscited by 5,931
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  7. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,611
  8. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  9. 2019Root Mean Square Layer Normalizationcited by 1,425
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 20163DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructionscited by 333
  12. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
25 more
  1. 2020PREDATOR: Registration of 3D Point Clouds with Low Overlapcited by 287
  2. 2023Flow Matching on General Geometriescited by 260
  3. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  4. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  5. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 204
  6. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  7. 2022Geometric Transformer for Fast and Robust Point Cloud Registrationcited by 200
  8. 2022e3nn: Euclidean Neural Networkscited by 171
  9. 2022CroCo: Self-Supervised Pre-training for 3D Vision Tasks by Cross-View Completioncited by 158
  10. 2023Equivariant flow matchingcited by 131
  11. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  12. 2020Learning multiview 3D point cloud registrationcited by 78
  13. 2023Rotation-Invariant Transformer for Point Cloud Matchingcited by 68
  14. 2020Generative 3D Part Assembly via Dynamic Graph Learningcited by 65
  15. 2023Equivariant Flow Matching with Hybrid Probability Transportcited by 59
  16. 2022Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learningcited by 54
  17. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
  18. 2022Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priorscited by 42
  19. 2022Breaking Bad: A Dataset for Geometric Fracture and Reassemblycited by 38
  20. 2023Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assemblycited by 27
  21. 2023Jigsaw: Learning to Assemble Multiple Fractured Objectscited by 26
  22. 2021HARA: A Hierarchical Approach for Robust Rotation Averagingcited by 22
  23. 2025GARF: Learning Generalizable 3D Reassembly for Real-World Fracturescited by 12
  24. 2023Adaptive Multi-step Refinement Network for Robust Point Cloud Registrationcited by 4
  25. 2024SE(3)-bi-equivariant Transformers for Point Cloud Assemblycited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Rectified Point Flow: Generic Point Cloud Pose Estimationcited by 13
  2. 2026Equivariant Latent Alignment via Flow Matching under Group Symmetriescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025E-M3RF: An Equivariant Multimodal 3D Re-assembly Framework
  2. 2025Leveraging Pretrained Diffusion Models for Zero-Shot Part Assembly
  3. 2025Assembler: Scalable 3D Part Assembly via Anchor Point Diffusion
  4. 2026TORA: Topological Representation Alignment for 3D Shape Assembly
  5. 2026MeshFlow: Mesh Generation with Equivariant Flow Matching
  6. 2026Hierarchical Flow Matching for 3D Point Cloud Generation
  7. 2026Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometries
  8. 2026EquiForm: Noise-Robust SE(3)-Equivariant Policy Learning from 3D Point Clouds