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DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly
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Proposes DiffAssemble, a graph-diffusion model that denoises piece poses with an attention-based GNN (UniMP + Exphormer sparsification) to solve both 2D jigsaw puzzles and 3D fractured-object reassembly.
Problem
Reassembly tasks (2D jigsaw puzzles with translated and rotated pieces, and 3D fractured object reassembly) are usually solved by separate methods, and learning-based methods have lagged optimization methods in 2D or in 3D rotation/translation accuracy.
Approach
Treat pieces as nodes of a complete graph with equivariant features and noisy pose (translation + rotation); train a DDIM-style diffusion model where an attention-based GNN (UniMP) predicts clean poses, with Exphormer sparsification to scale to up to 900 pieces.
Key results
- On Breaking Bad everyday objects, DiffAssemble reaches RMSE(R) 73.3 and RMSE(T) 14.8 and Part Accuracy 27.5%, beating SE(3)-Equiv (77.9, 16.7, 8.1%).
- On PuzzleCelebA 12x12 jigsaw, DiffAssemble scores 97.76% vs 93.33% for the best optimization baseline (Yu et al.), while on PuzzleWikiArt optimization methods remain better.
- Solves 30x30 (900-piece) puzzles in about 5 s at roughly 95% accuracy, versus 55 s with 58% accuracy for Gallagher; sparsity halves memory at 900 elements.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the diffusion process (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 3.1 -> 27.5 | Helped |
| add rotation-equivariant features (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 18.3 -> 27.5 | Helped |
| use rotation-equivariant rather than non-equivariant features (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 18.32 -> 27.48 | Helped |
| use equivariant rather than invariant features (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 14.27 -> 27.48 | Helped |
| use the SO(3) diffusion design rather than 6 degree-of-freedom rotation (ablation) | DiffAssemble · Breaking Bad everyday object subset | RMSE (R) (degree): 75.60 -> 73.34 | Helped |
| add Chamfer Distance loss (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 24.10 -> 27.48 | Helped |
| use attention-based UniMP rather than standard GCN (ablation) | DiffAssemble · Breaking Bad everyday object subset | Part Accuracy (%): 21.33 -> 27.48 | Helped |
| retain the diffusion process (ablation) | DiffAssemble · PuzzleCelebA 8×8 | Direct comparison accuracy: 79.84 -> 87.66 | Helped |
| retain the equivariant encoder (ablation) | DiffAssemble · PuzzleWikiArts 12×12 | Direct comparison accuracy: 4.96 -> 53.08 | Helped |
| use DiffAssemble rather than the strongest optimization baseline | PuzzleCelebA · 6×6 and 8×8 puzzles | Direct comparison accuracy: 98.63 -> 99.51; 97.45 -> 87.66 | Mixed |
| use DiffAssemble rather than the strongest optimization baseline | PuzzleWikiArts · PuzzleWikiArts | Direct comparison accuracy: 94.62 -> 90.65 | Hurt |
| remove 30% of the puzzle pieces | DiffAssemble · PuzzleCelebA 6×6 | Direct comparison accuracy: 99.51 -> 96.92 | Hurt |
Surprising findings
- Optimization-based methods drop sharply with 30% missing pieces, while DiffAssemble retains high accuracy on PuzzleCelebA (e.g., 96.92% at 6x6).
- Without the diffusion process, part accuracy on Breaking Bad falls from 27.5% to 3.1%, showing the multi-step denoising is critical.
Limitations
- High GPU memory usage even with expander-graph sparsification.
- Underperforms optimization methods on WikiArt puzzles, attributed to reliance on semantic content.
- Struggles with small fragments in 3D reassembly.
Experimental setup
Datasets: Breaking Bad PuzzleCelebA PuzzleWikiArt
Benchmarks: Breaking Bad PuzzleCelebA PuzzleWikiArt
Metrics: RMSE (R) RMSE (T) Part Accuracy direct comparison accuracy run-time GPU memory
Baselines: Global DGL LSTM NSM SE(3)-Equiv Gallagher Yu et al. Huroyan et al. GCN
Builds on: DDIM UniMP Exphormer VN-DGCNN Breaking Bad
Closest papers by meaning
- PuzzleFusion++: Auto-agglomerative 3D Fracture Assembly by Denoise and Verify (ICLR 2025 · similarity 0.85)
- PHFormer: Multi-Fragment Assembly Using Proxy-Level Hybrid Transformer (AAAI 2024 · similarity 0.83)
- Neural Assembler: Learning to Generate Fine-Grained Robotic Assembly Instructions from Multi-View Images (AAAI 2025 · similarity 0.83)
- A machine learning approach that beats Rubik's cubes (NeurIPS 2025 · similarity 0.83)
- Reconstructing the Image Stitching Pipeline: Integrating Fusion and Rectangling into a Unified Inpainting Model (NeurIPS 2024 · similarity 0.83)
- Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving (NeurIPS 2024 · similarity 0.83)
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