# Rectified Point Flow: Generic Point Cloud Pose Estimation

arXiv: https://arxiv.org/abs/2506.05282 · HTML: https://mlsanity.com/paper/2506.05282/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 73 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 30 of 58)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [BOP: Benchmark for 6D Object Pose Estimation](https://mlsanity.com/paper/1808.08319/) (2018)
- [Real-Time Seamless Single Shot 6D Object Pose Prediction](https://mlsanity.com/paper/1711.08848/) (2017)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [BOP Challenge 2020 on 6D Object Localization](https://mlsanity.com/paper/2009.07378/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)

## Built on by (most cited first, 14 of 14)

- [Register Any Point: Scaling 3D Point Cloud Registration by Flow Matching](https://mlsanity.com/paper/2512.01850/) (2025)
- [TORA: Topological Representation Alignment for 3D Shape Assembly](https://mlsanity.com/paper/2604.04050/) (2026)
- [Dense associative memory for Gaussian distributions](https://mlsanity.com/paper/2509.23162/) (2025)
- [HomoFM: Deep Homography Estimation with Flow Matching](https://mlsanity.com/paper/2601.18222/) (2026)
- [Generative 6D Pose Estimation via Conditional Flow Matching](https://mlsanity.com/paper/2602.19719/) (2026)
- [CRAG: Can 3D Generative Models Help 3D Assembly?](https://mlsanity.com/paper/2602.22629/) (2026)
- [SARe: Structure-Aware Generative 3D Fragment Reassembly](https://mlsanity.com/paper/2603.21611/) (2026)
- [ReSeFlow: Rectifying SE(3)-Equivariant Policy Learning Flows](https://mlsanity.com/paper/2509.22695/) (2025)
- [LAMP: Lift Image-Editing as General 3D Priors for Open-world Manipulation](https://mlsanity.com/paper/2604.08475/) (2026)
- [Foundational feature fusion for conditional flow matching in 6D pose estimation](https://mlsanity.com/paper/2608.29183/) (2026)
- [BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration](https://mlsanity.com/paper/2609.11472/) (2026)
- [PART: Learning 3D Part Assembly and Retrieval with Transformers](https://mlsanity.com/paper/2609.19872/) (2026)
- [AssemblyWorld: Rethinking 3D Assembly with General-Purpose Agents](https://mlsanity.com/paper/2609.40353/) (2026)
- [LLM2R: From Large Language Models to 3D Reassemblers](https://mlsanity.com/paper/2610.18604/) (2026)

## Abstract (arXiv)

We introduce Rectified Point Flow, a unified parameterization that formulates pairwise point cloud registration and multi-part shape assembly as a single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part-wise poses with ad-hoc symmetry handling, our method intrinsically learns assembly symmetries without symmetry labels. Together with a self-supervised encoder focused on overlapping points, our method achieves a new state-of-the-art performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training on diverse datasets, facilitating the learning of shared geometric priors and consequently boosting accuracy. Project page: https://rectified-pointflow.github.io/.