TORA: Topological Representation Alignment for 3D Shape Assembly

Paper | Project Page | Code

TORA is a topology-first representation alignment framework for 3D shape assembly. It distills relational structure from a frozen pretrained 3D encoder into a flow-matching backbone during training. By matching the similarity structure between student and teacher representations (using CKA loss), TORA achieves faster convergence and improved accuracy for assembling unposed 3D parts into complete objects.

Overview

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations. TORA introduces zero inference overhead while yielding two consistent benefits:

• Faster convergence: Up to 6.9x faster training.
• Improved accuracy: Better performance in-distribution and greater robustness under domain shift.
• Zero overhead: The teacher alignment occurs only during training.

Usage

For detailed setup and training instructions, please refer to the official GitHub repository.

Evaluation

To run evaluation on a trained TORA model, you can use the following command:

python sample.py \
    ckpt_path=./output/TORA_base/best.ckpt \
    data_root="../dataset" \
    data=main/bbad_everyday

Citation

@article{lee2026tora,
  title     = {TORA: Topological Representation Alignment for 3D Shape Assembly},
  author    = {Lee, Nahyuk and Chen, Zhiang and Pollefeys, Marc and Hong, Sunghwan},
  journal   = {arXiv preprint arXiv:2604.04050},
  year      = {2026}
}