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 5.9×) 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.
TORA outperforms RPF in every setting—geometric, semantic, and inter-object. Higher Part Accuracy ↑ is better; lower Rotation Error ↓ and Translation Error ↓ are better.
Drag the slider to control the flow from noise (disassembled) to assembled state.
TORA consistently accelerates optimization, reaching the RPF baseline's peak performance up to 5.9× faster.
Geometry- and contact-centric properties predict assembly transfer, not semantic classification ability.
We adopt Uni3D as the default teacher, as it consistently achieves the strongest geometry/contact probe performance and yields the best downstream assembly accuracy across all alignment objectives.
@inproceedings{anonymous2026tora,
title = {TORA: Topological Representation Alignment
for 3D Shape Assembly},
author = {Lee, Nahyuk and Chen, Zhiang and Pollefeys, Marc and Hong, Sunghwan},
year = {2026}
}