# TORA: Topological Representation Alignment for 3D Shape Assembly arXiv: https://arxiv.org/abs/2604.04050 · HTML: https://mlsanity.com/paper/2604.04050/ ## Key facts - Cited by 4 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 58 of its 74 references that are in the map. - First posted on arXiv 5 Apr 2026. ## 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 58) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020) - [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023) - [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022) - [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017) - [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023) - [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015) - [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022) - [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017) - [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024) - [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021) - [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023) - [ABO: Dataset and Benchmarks for Real-World 3D Object Understanding](https://mlsanity.com/paper/2110.06199/) (2021) - [3D-FUTURE: 3D Furniture shape with TextURE](https://mlsanity.com/paper/2009.09633/) (2020) - [BOP: Benchmark for 6D Object Pose Estimation](https://mlsanity.com/paper/1808.08319/) (2018) - [Uni3D: Exploring Unified 3D Representation at Scale](https://mlsanity.com/paper/2310.06773/) (2023) - [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025) - [CAT-Seg: Cost Aggregation for Open-Vocabulary Semantic Segmentation](https://mlsanity.com/paper/2303.11797/) (2023) - [OpenShape: Scaling Up 3D Shape Representation Towards Open-World Understanding](https://mlsanity.com/paper/2305.10764/) (2023) - [Cost Aggregation with 4D Convolutional Swin Transformer for Few-Shot Segmentation](https://mlsanity.com/paper/2207.10866/) (2022) - [Sonata: Self-Supervised Learning of Reliable Point Representations](https://mlsanity.com/paper/2503.16429/) (2025) - [Representation Entanglement for Generation: Training Diffusion Transformers Is Much Easier Than You Think](https://mlsanity.com/paper/2507.01467/) (2025) - [Geometry Forcing: Marrying Video Diffusion and 3D Representation for Consistent World Modeling](https://mlsanity.com/paper/2507.07982/) (2025) - [What matters for Representation Alignment: Global Information or Spatial Structure?](https://mlsanity.com/paper/2512.10794/) (2025) - [CATs: Cost Aggregation Transformers for Visual Correspondence](https://mlsanity.com/paper/2106.02520/) (2021) - [Generative 3D Part Assembly via Dynamic Graph Learning](https://mlsanity.com/paper/2006.07793/) (2020) - [PF3plat: Pose-Free Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2410.22128/) (2024) - [CATs++: Boosting Cost Aggregation with Convolutions and Transformers](https://mlsanity.com/paper/2202.06817/) (2022) - [Form2Fit: Learning Shape Priors for Generalizable Assembly from Disassembly](https://mlsanity.com/paper/1910.13675/) (2019) - [Concerto: Joint 2D-3D Self-Supervised Learning Emerges Spatial Representations](https://mlsanity.com/paper/2510.23607/) (2025) ## Built on by (most cited first, 4 of 4) - [No Pose, No Problem in 4D: Feed-Forward Dynamic Gaussians from Unposed Multi-View Videos](https://mlsanity.com/paper/2605.22190/) (2026) - [Learning Global Motion with Compact Gaussians for Feed-Forward 4D Reconstruction](https://mlsanity.com/paper/2605.31595/) (2026) - [PROSE: Training-Free Egocentric Scene Registration with Vision-Language Models](https://mlsanity.com/paper/2606.16569/) (2026) - [AssemblyWorld: Rethinking 3D Assembly with General-Purpose Agents](https://mlsanity.com/paper/2609.40353/) (2026) ## Abstract (arXiv) Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9×) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.