MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation
Organizations: University at Buffalo, SUNY, USA · National Institutes of Health, USA · POSTECH, South Korea
Abstract
Functional brain connectome represents neural connectivity as a matrix of pairwise interactions between brain regions. Generation of functional connectomes is not only a question of validity; rather, having satisfied the constraints on the correlation matrix, the next step is to recover the class-conditional geometry buried under coarse labels. We propose MAGNET, a Manifold-Aware Graph Diffusion Network which uses a normalized-Cholesky representation of the manifold of correlation matrices that guarantees validity. MAGNET lifts noisy latent states into ROI-level region tokens and performs denoising with a relational inductive bias over brain atlas regions. To deal with structural problems induced by coarse labels, MAGNET employs class-anchored conditioning, amortized structural bridge, and relevance-preserving corruption. Across ABIDE, ADNI, and OASIS-3, MAGNET consistently achieves favorable results compared to previous manifold-aware approaches, demonstrating improvements of 7-21% in class-conditional fidelity (-F1) across three cohorts and better sampling efficiency. Moreover, while training only with strict binary labels, MAGNET is capable of maintaining clinical heterogeneity through fine substructure of the connectomes in a zero-shot setting, improving subclass covariance alignment (-MSE) by over 30%. These results suggest that geometric validity is a necessary but insufficient condition for clinical utility in connectome synthesis. Moreover, efforts in making the diffusion denoising class-conditional manifold aware finds utility beyond the highly curved brain connectome generation as this is a critical problem in various general settings. The code repository can be found at https://github.com/protyayofficial/MAGNET.
Figures & tables
| Dataset | Method | Quality Metrics | CAS Metrics | Time (s.) | |||
|---|---|---|---|---|---|---|---|
| -Precision | -Recall | -F1 | ROC-AUC | F1 | Sampling | ||
| ABIDE | Real Data | 0.80 0.04 | 0.81 0.04 | 0.80 0.01 | 0.66 0.04 | 0.58 0.06 | N/A |
| TriangCFM | 0.21 0.21 | 0.24 0.35 | 0.20 0.29 | 0.50 0.05 | 0.40 0.13 | 7.16 1.17 | |
| TriangDDPM | 0.25 0.04 | 0.22 0.06 | 0.23 0.04 | 0.52 0.05 | 0.43 0.08 | 5.45 0.19 | |
| DiffeoGauss | 0.51 0.04 | 0.23 0.03 | 0.32 0.03 | 0.66 0.05 | 0.56 0.06 | 0.06 0.01 | |
| DiffeoCFM | 0.81 0.05 | 0.50 0.04 | 0.62 0.05 | 0.60 0.04 | 0.52 0.07 | 9.04 0.86 | |
| Method | Quality (Macro-Averaged) | CAS | Distributional Preservation | |||||
|---|---|---|---|---|---|---|---|---|
| -Prec. | -Recall | -F1 | Macro F1 | Class | Class | -MSE | ||
| ADNI | TriangCFM | |||||||
| DiffeoGauss | ||||||||
| DiffeoCFM | ||||||||
| GDSS-proj | ||||||||
| MAGNET (ours) | ||||||||
| Dataset | Backbone | Controller | Quality | Sampling (s.) | |||||
|---|---|---|---|---|---|---|---|---|---|
| Subtype | Bridge | Noise | Guidance | -Prec. | -Rec. | -F1 | |||
| ABIDE | Vector | ✗ | ✗ | ✗ | ✗ | ||||
| Graph | ✗ | ✗ | ✗ | ✗ | |||||
| Graph | ✓ | ✗ | ✗ | ✗ | |||||
| Graph | ✗ | ✓ | ✗ | ✗ | |||||
| Graph | ✗ | ✗ | ✓ | ✗ | |||||
| Atlas | Method | -Prec. | -Rec. | -F1 | ROC-AUC | F1 | Time (s) |
|---|---|---|---|---|---|---|---|
| AAL116 | Real Data | 0.78 0.06 | 0.77 0.09 | 0.77 0.05 | 0.72 0.09 | 0.63 0.07 | N/A |
| TriangCFM | 0.34 0.09 | 0.02 0.01 | 0.04 0.02 | 0.49 0.05 | 0.42 0.19 | 3.80 0.21 | |
| TriangDDPM | 0.41 0.05 | 0.12 0.07 | 0.37 0.08 | 0.53 0.08 | 0.48 0.12 | 3.21 0.32 | |
| DiffeoGauss | 0.55 0.05 | 0.35 0.07 | 0.43 0.05 | 0.53 0.07 | 0.32 0.12 | 1.94 0.39 | |
| DiffeoCFM | 0.58 0.12 | 0.62 0.08 | 0.59 0.05 | 0.65 0.08 | 0.54 0.13 | 4.16 0.24 | |
| GDSS-proj | 0.05 0.02 | 0.21 0.01 | 0.08 0.03 | 0.51 0.03 | 0.34 0.09 | 1.43 0.12 |
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | Method | Quality | CAS Metrics | Bridge Distillation Error | Time (s.) | |
|---|---|---|---|---|---|---|
| - F1 | ROC-AUC | F1 | Sampling | |||
| ABIDE | Real Data | 0.80 0.01 | 0.66 0.04 | 0.58 0.06 | N/A | N/A |
| No bridge | 0.58 0.05 | 0.66 0.06 | 0.57 0.09 | - | 0.10 0.00 | |
| Self-conditioning | 0.51 0.06 | 0.66 0.06 | 0.56 0.11 | - | 3.01 0.01 | |
| Teacher bridge | 0.64 0.06 | 0.66 0.06 | 0.57 0.09 | - | 3.00 0.01 | |
| Amortized bridge ( ) | 0.65 0.05 | 0.66 0.05 | 0.57 0.08 | 0.48 0.04 | 0.12 0.00 | |
| Dataset | Configuration | Decay ( ) | Quality | CAS Metrics | Sampling Time (s) | |
|---|---|---|---|---|---|---|
| -F1 | ROC-AUC | F1 | ||||
| ABIDE | Isotropic (Baseline) | N/A | ||||
| Low Density | 1 | |||||
| Adaptive (Ours) | 3 | |||||
| High Density | 5 | |||||
| ADNI | Isotropic (Baseline) | N/A | ||||
| Dataset | sensitivity | sensitivity | ||||||
|---|---|---|---|---|---|---|---|---|
| -F1 | ROC-AUC | F1 | -F1 | ROC-AUC | F1 | |||
| ABIDE | 0 | 0.51 0.04 | 0.52 0.06 | 0.43 0.01 | 0 | 0.53 0.03 | 0.56 0.06 | 0.41 0.09 |
| 0.025 | 0.66 0.06 | 0.62 0.09 | 0.55 0.03 | 0.025 | 0.66 0.05 | 0.63 0.05 | 0.55 0.06 | |
| 0.05 | 0.67 0.01 | 0.62 0.06 | 0.55 0.09 | 0.05 | 0.66 0.03 | 0.64 0.08 | 0.55 0.05 | |
| 0.1 (default) | 0.68 0.03 | 0.64 0.07 | 0.56 0.06 | 0.1 (default) | 0.68 0.03 | 0.64 0.07 | 0.56 0.06 | |
| 0.2 | 0.67 0.02 | 0.63 0.02 | 0.56 0.12 | 0.2 | 0.66 0.03 | 0.64 0.02 | 0.54 0.01 | |
| Data | CI | Real | MAGNET | D-CFM | D-Gauss |
|---|---|---|---|---|---|
| ABIDE | C0 | 4.22 | 4.65 (+.43) | 4.76 (+.53) | 5.05 (+.83) |
| C1 | 4.17 | 4.70 (+.54) | 4.85 (+.68) | 5.15 (+.98) | |
| ADNI | C0 | 5.54 | 7.15 (+1.6) | 7.43 (+1.9) | 10.1 (+4.5) |
| C1 | 5.62 | 7.80 (+2.2) | 7.71 (+2.1) | 10.5 (+4.9) | |
| OASIS | C0 | 4.84 | 5.27 (+.43) | 5.54 (+.70) | 5.83 (+.98) |
| C1 | 4.88 | 5.35 (+.48) | 5.70 (+.82) | 5.98 (+1.1) |
| Dataset | Class | MAGNET | D-CFM | T-CFM | D-Gauss |
|---|---|---|---|---|---|
| ABIDE | Class 0 | 1.000 | 0.879 | 0.008 | 0.996 |
| Class 1 | 1.000 | 0.787 | 0.008 | 0.983 | |
| Avg. | 1.000 | 0.833 | 0.008 | 0.990 | |
| ADNI | Class 0 | 0.896 | 0.762 | 0.000 | 0.083 |
| Class 1 | 0.821 | 0.721 | 0.000 | 0.029 | |
| Avg. | 0.859 | 0.742 | 0.000 | 0.056 |
Functional Connectivity
Functional connectivity measures statistical relationships between brain regions to study how neural systems coordinate.
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