# E-M3RF: An Equivariant Multimodal 3D Re-assembly Framework

arXiv: https://arxiv.org/abs/2511.21422 · HTML: https://mlsanity.com/paper/2511.21422/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 27 of 27)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding](https://mlsanity.com/paper/2304.06906/) (2023)
- [Generative 3D Part Assembly via Dynamic Graph Learning](https://mlsanity.com/paper/2006.07793/) (2020)
- [Learning 3D Part Assembly from a Single Image](https://mlsanity.com/paper/2003.09754/) (2020)
- [Breaking Bad: A Dataset for Geometric Fracture and Reassembly](https://mlsanity.com/paper/2210.11463/) (2022)
- [DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly](https://mlsanity.com/paper/2402.19302/) (2024)
- [Jigsaw: Learning to Assemble Multiple Fractured Objects](https://mlsanity.com/paper/2305.17975/) (2023)
- [Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving](https://mlsanity.com/paper/2410.24010/) (2024)
- [Fantastic Breaks: A Dataset of Paired 3D Scans of Real-World Broken Objects and Their Complete Counterparts](https://mlsanity.com/paper/2303.14152/) (2023)
- [PuzzleFusion++: Auto-agglomerative 3D Fracture Assembly by Denoise and Verify](https://mlsanity.com/paper/2406.00259/) (2024)
- [GARF: Learning Generalizable 3D Reassembly for Real-World Fractures](https://mlsanity.com/paper/2504.05400/) (2025)
- [3D Geometric Shape Assembly via Efficient Point Cloud Matching](https://mlsanity.com/paper/2407.10542/) (2024)
- [Batch-based Model Registration for Fast 3D Sherd Reconstruction](https://mlsanity.com/paper/2211.06897/) (2022)
- [Fast(er) Reconstruction of Shredded Text Documents via Self-Supervised Deep Asymmetric Metric Learning](https://mlsanity.com/paper/2003.10063/) (2020)
- [ReassembleNet: Learnable Keypoints and Diffusion for 2D Fresco Reconstruction](https://mlsanity.com/paper/2505.21117/) (2025)

## Built on by (most cited first, 1 of 1)

- [AssemLM: A Spatial Reasoning Multimodal Large Language Model for Robotic Assembly](https://mlsanity.com/paper/2604.08983/) (2026)

## Abstract (arXiv)

3D reassembly is a fundamental geometric problem, and in recent years it has increasingly been challenged by deep learning methods rather than classical optimization. While learning approaches have shown promising results, most still rely primarily on geometric features to assemble a whole from its parts. As a result, methods struggle when geometry alone is insufficient or ambiguous, for example, for small, eroded, or symmetric fragments. Additionally, solutions do not impose physical constraints that explicitly prevent overlapping assemblies. To address these limitations, we introduce E-M3RF, an equivariant multimodal 3D reassembly framework that takes as input the point clouds, containing both point positions and colors of fractured fragments, and predicts the transformations required to reassemble them using SE(3) flow matching. Each fragment is represented by both geometric and color features: i) 3D point positions are encoded as rotationconsistent geometric features using a rotation-equivariant encoder, ii) the colors at each 3D point are encoded with a transformer. The two feature sets are then combined to form a multimodal representation. We experimented on four datasets: two synthetic datasets, Breaking Bad and Fantastic Breaks, and two real-world cultural heritage datasets, RePAIR and Presious, demonstrating that E-M3RF on the RePAIR dataset reduces rotation error by 23.1% and translation error by 13.2%, while Chamfer Distance decreases by 18.4% compared to competing methods.