MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation
cs.LG, cs.AI, cs.CV
Submitted: 2026-10-12
Updated: 2026-10-12
Comments: Accepted at NeurIPS 2026
Code: https://github.com/protyayofficial/MAGNET
License: http://creativecommons.org/licenses/by/4.0/
The gist: Functional brain connectome represents neural connectivity as a matrix of pairwise interactions between brain regions.
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 (α,β-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 (λ-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.
Sources
- Relational inductive biases, deep learning, and graph networks
- Diffusion Generative Modeling on Lie Group Representations
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
- Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning
- CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models
- Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction
- NIPS 2016 Tutorial: Generative Adversarial Networks
- Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries
- Manifold Preserving Guided Diffusion
- Distilling the Knowledge in a Neural Network
- Classifier-Free Diffusion Guidance
- Decoupling Representation and Classifier for Long-Tailed Recognition
- Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
- Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning
- A Kinetic Energy Perspective of Flow Matching
- Flow Matching for Generative Modeling
- Invariant and Equivariant Graph Networks
- Spectral Normalization for Generative Adversarial Networks
- Temporal Alignment Guidance: On-Manifold Sampling in Diffusion Models
- A Short Note on a Flexible Cholesky Parameterization of Correlation Matrices
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