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MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation

Protyay Dey, Ayush Roy, Hyuna Cho, Won Hwa Kim, Vishnu Suresh Lokhande

arXiv:2610.17014v2cs.LGcs.AIcs.CV

TL;DR

Coarse labels can conceal heterogeneous connectome subpopulations, so geometric validity alone does not ensure recovery of clinically appropriate class-conditional structure. MAGNET uses a normalized-Cholesky chart and region-level graph denoising with subtype conditioning, a structural bridge, and relevance-preserving corruption. Across three cohorts it reports improved fidelity, zero-shot clinical alignment, and few-step sampling efficiency over strong baselines.

  • Problem

    Coarse labels collapse structurally heterogeneous subpopulations, leaving support recovery distinct from—and not assured by—geometric validity.

    Source: §1 · p. 1, §2.1 · p. 3

  • Method

    MAGNET uses a normalized-Cholesky chart and ROI-level graph denoising, coupled with subtype conditioning, an amortized structural bridge, and relevance-preserving corruption.

    Source: §1 · pp. 2–3, §4 · p. 10

  • Results

    7–21% relative increase in class-conditional fidelity (α, β-F1) over the strongest validity-preserving baselines, with improvements reported across three cohorts.

    Source: §3.1 · p. 8, §4 · p. 10

  • Takeaways & Limitations

    Geometric validity is necessary but insufficient for structural recovery; conditional generation must also recover class-conditional organization within the valid correlation manifold.

    Source: §4 · p. 10

Abstract

from arXiv · show

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 ($\alpha,\beta$-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 ($\lambda$-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.

1 Introduction

Valid correlation matrices do not guarantee clinically faithful connectomes: coarse labels can conceal structurally diverse subpopulations, making class-conditional support recovery a central challenge. MAGNET combines a normalized-Cholesky chart, region-level graph denoising, and three mechanisms for addressing label ambiguity, missing global context, and coordinate corruption; it reports favorable fidelity, zero-shot subclass recovery, and sampling efficiency across three cohorts.

1 Introduction

  • Coarse labels collapse structurally diverse subpopulations, so geometrically valid samples can still miss the appropriate class-conditional regions of the connectome manifold.The introduction frames support recovery as distinct from geometric validity and notes that class distributions span off-axis directions rather than a single prototype.Source: §1 · pp. 1–2, Figure 2 · p. 2
  • Three challenges constrain support recovery: heterogeneous labels, insufficient global context under few reverse steps, and isotropic corruption that distorts informative chart coordinates.Standard classifier-free guidance can overspecialize and reduce coverage, while coordinate distortion makes class-conditional structure harder to recover in few-step regimes.Source: §1 · p. 2
  • Because normalized-Cholesky coordinates impose atlas ordering on a relational connectome, MAGNET uses region-token graph denoising to model structured dependencies.The introduction distinguishes this graph bias from permutation invariance: ordered Cholesky coefficients encode dependencies among regions.Source: §1 · p. 2
  • MAGNET combines class-anchored subtype conditioning, an amortized structural bridge, and relevance-preserving corruption to address label, global-context, and coordinate challenges.The bridge supplies subtype-specific structural summaries at reverse steps, while relevance-preserving corruption reduces noise on informative chart coordinates early.Source: §1 · p. 3
  • MAGNET reports robust conditional fidelity across ABIDE, ADNI, and OASIS-3, with superior zero-shot subclass recovery and accelerated sampling.The introduction points to ablations validating its three mechanisms and to empirical results across the three cohorts.Source: §1 · p. 3

2 Methodology

MAGNET combines a validity-preserving normalized-Cholesky chart with ROI-level graph denoising and three controllers aimed at recovering class-conditional structure. Its method also specifies a full training objective and a six-step sampling procedure.

2.1 From validity to support recovery

  • The normalized-Cholesky chart represents valid correlation connectomes and ensures decoded samples are symmetric, positive definite, and unit-diagonal.Diffusion operates on standardized chart coordinates rather than directly on correlation matrices.Source: §2.1 · p. 3

2.2 ROI-level graph denoising in the validity-preserving chart

  • MAGNET denoises ROI tokens with a Transformer, combining anatomical position with additive timestep, subtype, and bridge embeddings.Each token starts from a row of the reshaped noisy chart state; row projection and symmetrization map predictions back to chart coordinates.Source: §2.2 · p. 4

2.3.1 Class-anchored conditioning

  • A train-only subtype variable refines each coarse class, with generation sampling a subtype from its class-conditional distribution.Subtypes are fitted as Gaussian-mixture components in standardized chart coordinates and are intended to capture within-class structure, not a validated biological taxonomy.Source: §2.3.1 · pp. 4–5

2.3.2 Amortized structural bridge

  • The amortized structural bridge predicts a teacher-derived subtype feature target from the noisy state and replaces the teacher during inference.The bridge is injected into ROI-token conditioning; replacing the teacher yields an approximately 25–32× sampling speedup over teacher-bridge alternatives.Source: §2.3.2 · p. 5

2.3.3 Relevance-preserving corruption

  • Relevance-preserving corruption protects condition-relevant chart coordinates more strongly early in diffusion, then anneals toward standard isotropic noising.Coordinate relevance is estimated from the conditional–unconditional denoising gap, and the protection vanishes later in the trajectory.Source: §2.3.3 · p. 6

2.4 Full Training Objective

  • The full objective combines diffusion loss, bridge distillation error, and a structural-feature loss; sampling uses six DDIM reverse steps with subtype and bridge conditioning.The diffusion loss uses min-SNR reweighting and inverse subject-frequency weights for longitudinal cohorts.Source: §2.4 · p. 6

3 Experimental Results

MAGNET is evaluated across three neuroimaging cohorts, including binary-label benchmarks and a zero-shot test of fine-grained clinical structure. It outperforms validity-preserving baselines on class-conditional fidelity and preserves subclass structure, with gains also reported for ablations and higher-resolution atlases.

3.1 Main Benchmark

  • Up to 21% relative increase in class-conditional fidelity (α, β-F1) over the strongest validity-preserving baselines, with gains of 21% on OASIS-3 and 7% on ADNI.MAGNET also achieves the highest or tied-best classifier-based F1 across all three cohorts and generates faster than flow-matching baselines; the amortized bridge yields an additional approximately 25–32× reduction relative to teacher-bridge alternatives.Source: §3.1 · p. 8

3.2 Zero-Shot Recovery of Fine-Grained Clinical Subclasses

  • 33–57% reduction in λ-MSE on ADNI relative to baselines in the zero-shot evaluation of subclass covariance alignment.MAGNET also attains the best macro β-recall, α, β-F1, and CAS macro-F1 on ADNI, and sweeps the support-recovery, CAS, and λ-MSE metrics on OASIS-3.Source: §3.2 · p. 9

3.3 Graph Backbone and Controller Necessity

  • The graph denoiser improves results over a vector denoiser, while the amortized bridge is the largest individual controller contributor, raising ADNI α, β-F1 from 0.57 to 0.69.The ablation uses the same normalized-Cholesky validity chart and a six-step sampling budget; the graph backbone supplies ROI-relational inductive bias absent from the chart alone.Source: §3.3 · p. 9, Table 3 · p. 9
  • 17% and 14% relative gains in α, β-F1 over DiffeoCFM on the AAL116 and CC200 atlases, respectively.Both higher-resolution evaluations use the same quality-controlled 831-scan ABIDE cohort and 10-split group-aware protocol.Source: §3.3 · p. 10, Table 4 · p. 10

4 Conclusion

The conclusion frames connectome synthesis as requiring more than geometric validity: models must recover class-conditional organization within the valid correlation manifold. MAGNET combines a region-level graph denoiser with mechanisms for coarse-label ambiguity, missing global context, and condition-relevant coordinates; the authors identify broader evaluation and input directions for future work.

4 Conclusion

  • MAGNET combines an ROI-level graph denoiser with class-anchored subtype conditioning, an amortized structural bridge, and relevance-preserving corruption to address ambiguity in conditional support recovery.The conclusion reports improved distributional fidelity, support recovery, zero-shot clinical alignment, and few-step sampling efficiency over strong baselines across three cohorts.Source: §4 · p. 10
  • The authors identify multimodal imaging, longitudinal trajectory generation, and downstream clinical-prediction utility as future directions.They also suggest that amortized structural summaries for fast inference may extend to constrained generative settings beyond connectomes.Source: §4 · p. 10

B.1 Proof of Proposition 1

The proof uses squared-loss conditional-mean predictors to show how access to a subtype variable can reduce denoising risk when it resolves structure hidden by the coarse label.

B.1 Proof of Proposition 1

  • For squared loss, the coarse- and subtype-conditioned Bayes estimators are conditional means, and their residual decomposition has a vanishing cross term.The resulting risk gain is strictly positive whenever the subtype resolves within-class structure that the coarse label does not.Source: §B.1 · p. 18
  • The gain is zero exactly when the subtype provides no additional information beyond the coarse label.The paper reports that its heterogeneity-entropy analysis finds nonzero gains that scale with dataset complexity.Source: §B.1 · p. 18

B.2 Proof of Proposition 2

The proposition proof bounds the effect of replacing a teacher bridge with an amortized predictor, while the following surrogate result motivates protecting class-relevant directions during corruption. The bridge bound relies on a distributional smoothness assumption that compactness alone does not establish.

B.2 Proof of Proposition 2

  • The amortization bound follows by decomposing the plug-in predictor error and using a vanishing cross term, then applying the assumed Lipschitz property of the Bayes regressor in its bridge argument.The paper distinguishes this distributional assumption from the deployed bridge network’s finite Lipschitz constant.Source: §B.2 · pp. 18–19
  • The bridge input lies in a bounded convex hull of atoms, but compactness does not imply that the Bayes regressor is Lipschitz there.A sufficient condition given is continuous differentiability with uniformly bounded Jacobian on a neighborhood of the relevant domain.Source: §B.2 · p. 19
  • The amortized bridge tracks a teacher target to provide structural context that an isolated noisy state may lack under few-step sampling, with up to approximately 25–32× sampling-cost savings reported.The stated role differs from traditional distillation, which shrinks capacity in the same output space.Source: §B.2 · p. 19

B.3 A surrogate result for relevance-preserving corruption

  • Under a Gaussian surrogate, protecting class-relevant directions is preferable to isotropic corruption when the reverse budget is small.In the full model, the relevant directions are estimated from the guidance signal rather than assumed known.Source: §B.3 · p. 20

C Baselines

The baselines separate validity-preserving geometry, learned transport, and structure-aware conditional recovery. An adapted generic graph diffusion model provides a comparison but requires projection to produce valid connectomes.

C Baselines

  • The baselines use the same splits, preprocessing, and sampling budgets as MAGNET, isolating model design from data handling and integration depth.Source: C Baselines · p. 21
  • DiffeoCFM tests whether conditional flow matching in a normalized-Cholesky pullback chart is sufficient for connectome generation.Source: C Baselines · p. 21
  • DiffeoGauss replaces DiffeoCFM’s learned transport with a class-conditional Gaussian model, isolating learned flow dynamics while retaining its geometry.Source: C Baselines · p. 21
  • TriangCFM uses continuous flow matching on strict lower-triangular coordinates without a validity-preserving chart, then projects samples onto the correlation manifold.Source: C Baselines · p. 21
  • Generic discrete-edge graph generators are excluded because dense continuous-valued connectomes require different representations, denoising objectives, and output constraints.The authors state that adapting these models would make comparisons difficult to interpret.Source: C Baselines · p. 21
  • GDSS-proj substantially underperforms validity-aware generators on support fidelity and zero-shot subclass recovery, despite fast sampling.It applies post-hoc projection to dense signed ROI adjacency outputs to enforce correlation-matrix structure.Source: C Baselines · p. 21

D Experimental Setup

The setup evaluates support fidelity, downstream utility, and subclass covariance alignment across matched splits and sampling budgets. MAGNET combines region-token denoising with structural conditioning, then tests bridge, corruption, guidance, and conditioning choices.

D Experimental Setup

  • MAGNET evaluates α-precision, β-recall, their harmonic mean α, β-F1, downstream ROC-AUC and F1, and zero-shot subclass covariance alignment with λ-MSE.The metric protocol uses 10 disjoint train/validation splits, subject-level disjointness for ADNI and OASIS-3, and matched six-step sampling budgets.Source: D Experimental Setup · pp. 21–22

E Architectural Details

  • The denoiser converts chart coordinates into ROI row tokens, applies attention across regions, and maps its output back to the normalized-Cholesky chart.Tokens combine connectivity profiles, ROI identity, and conditioning; conditioning includes timestep, subtype, and bridge embeddings, while class-wise latent calibration precedes chart decoding.Source: E Architectural Details · pp. 22–23

F.1 Amortized Structural Bridge

  • Bridge-enabled MAGNET variants retain roughly 30–60× lower sampling cost than teacher-bridge and self-conditioned alternatives while delivering the strongest overall fidelity profile.Lower bridge distillation error tracks stronger α, β-F1; removing bridge supervision causes severe tracking failure.Source: §F.1 · p. 23, Table 5 · p. 23

F.2 Relevance-Preserving Corruption Ablation

  • Across ABIDE, ADNI, and OASIS-3, adaptive protection improves over isotropic diffusion, while fidelity and downstream utility remain stable across p = 1, 3, and 5.The schedule shields condition-defining coordinates early in diffusion; its decay parameter controls when structural coordinates yield to noise.Source: §F.2 · p. 24, Table 6 · p. 24

F.3 Classifier-Free Guidance Scale

  • On ADNI, γ = 1.5 gives the best overall fidelity–utility trade-off; stronger guidance raises α-precision but sharply lowers β-recall.OASIS-3 follows a similar, less sharp pattern; ABIDE is less sensitive once guidance is enabled. Figure 5 compares α-precision, β-recall, and CAS F1 across cohorts.Source: E Architectural Details · p. 22, Figure 5 · p. 24, §F.3 · p. 25

F.4 Class-Anchored Conditioning

  • Class-Anchored Conditioning models each class as a Gaussian mixture with subtype tokens, and its gain over class-only and clustering baselines scales with structural heterogeneity H.H measures the entropy of discovered structural subtypes conditioned on coarse labels.Source: Figure 6 · p. 25, §F.4 · p. 25

F.5 Self-conditioning probability

  • Varying fallback self-conditioning probability from 0.2 to 0.8 produces no meaningful fidelity or downstream-performance change across the three cohorts.The final configuration primarily uses the amortized bridge, and the paper fixes psc = 0.5.Source: §F.5 · p. 25

F.6 Training and Sampling Efficiency

MAGNET exchanges higher one-time training cost for faster repeated sampling while improving conditional fidelity. Its auxiliary losses contribute to support recovery, but their nonzero weights need not be narrowly tuned.

F.6 Training and Sampling Efficiency

  • MAGNET improves α, β-F1 by 7–21% over the strongest validity-preserving baseline across primary cohorts while sampling roughly 24×, 42×, and 37× faster on ABIDE, ADNI, and OASIS-3.Training takes roughly an order of magnitude longer than DiffeoCFM and TriangCFM under the reported hardware setting; MAGNET sampling takes 0.38 s, 0.86 s, and 0.63 s per split, respectively.Source: §F.6 · p. 26

F.7 Sensitivity to λbridge and λspec

  • Removing either auxiliary loss degrades α, β-F1, while nonzero loss-weight sweeps show only small performance variation across cohorts.Removing the spectral term changes α, β-F1 from 0.68 to 0.51 on ABIDE, 0.76 to 0.68 on ADNI, and 0.57 to 0.49 on OASIS-3; removing bridge supervision reduces it to 0.53, 0.65, and 0.42, respectively. Across nonzero sweeps, variation is at most 0.02 for λspec and 0.03 for λbridge; the default 0.1 weights lie in a broad stable region.Source: §F.7 · p. 26

G Geometric Analysis of Conditional Connectome Generation

The geometric analysis compares generated and held-out real connectomes within each class. It fixes evaluation references using real data and uses a log-Euclidean representation to assess distributional agreement.

G.1 Visualization Setup

G.2 Geometry, Assumptions, and why this analysis

  • Connectomes are mapped with the matrix logarithm into symmetric-matrix space, where Euclidean comparisons use the Frobenius norm.The log-Euclidean representation is used because ordinary Euclidean operations on correlation matrices do not faithfully capture their geometry.Source: §G.2 · p. 27
  • The visualization assumes valid positive-definite connectomes, class-conditional evaluation, real-derived reference geometry, and locally regular held-out support for nearest-neighbor spacing.These assumptions keep visual objects fixed across methods and support interpretation alongside summary statistics.Source: §G.2 · pp. 27–28

G.3 Global geometric fidelity through radial calibration

Radial calibration maps connectomes to distances from the held-out real class center to assess global geometric alignment. MAGNET has the closest radial-distribution alignment across datasets, but radial agreement alone does not guarantee full geometric fidelity.

G.3 Global geometric fidelity through radial calibration

  • Radial analysis maps each manifold-valued distribution to a one-dimensional law of distances from the held-out real class center.The class center is the log-Euclidean Fréchet mean, derived from the mean of log-domain connectomes.Source: §G.3 · p. 28
  • The held-out real log-Euclidean Fréchet mean minimizes expected squared log-Euclidean distance to the held-out real distribution.The proof relaxes the optimization to the ambient symmetric-matrix space and obtains the mean of the matrix logarithms.Source: §G.3 · pp. 28–29
  • Matching radial laws is necessary but insufficient for full distribution agreement because the radial mapping discards directional information.Distributions can share radial profiles while occupying different directional regions, so radial calibration must be paired with directional or topological evaluations.Source: §G.3 · p. 29
  • MAGNET achieves the smallest deviation from the held-out real center across all three datasets, while TriangCFM shows severe overdispersion.TriangCFM is excluded from Table 8 because its median radial distances exceed 40 units and fall outside the remaining methods’ axis range.Source: §G.3 · p. 29, Figure 7 · p. 30

G.4 Local Support Occupancy via Tangent Charts

Tangent-chart occupancy evaluates whether generated connectomes fall within support defined by held-out real data, complementing global radial calibration. MAGNET attains the highest inside-support rate across datasets and finishes reverse-time denoising with tighter support alignment.

G.4 Local Support Occupancy via Tangent Charts

  • The tangent chart uses held-out real connectomes to define its basis, and generated samples are projected into that chart without defining it.The support region approximates the central 90% of held-out real chart data; inside-support rate is the fraction of generated samples within that region.Source: §G.4 · pp. 30–31
  • MAGNET localizes generated density inside the dominant held-out real support contour and achieves the highest inside-support rate across datasets.TriangCFM shows near-zero inside-support rates across clinical cohorts; DiffeoGauss projects beyond the true contours on heterogeneous ADNI, while DiffeoCFM leaks mass just outside real boundaries.Source: §G.4 · pp. 31, 33, Figure 8 · p. 32, Table 9 · p. 33

H Reverse-time refinement

  • Reverse-time trajectories project each denoising checkpoint into the same held-out real tangent chart to track movement relative to real support.The analysis does not assume inside-support rate changes monotonically over time.Source: §H.1 · p. 33

H.1 Reverse-time tangent-manifold trajectory

  • DiffeoCFM enters the vicinity of real support earlier, but MAGNET finishes with tighter support alignment in the second half of reverse-time denoising.On OASIS-3, DiffeoCFM’s inside-support rate decays mildly from 1.00 to 0.91 while MAGNET remains near the real support contour; on ABIDE, both methods stay inside support throughout.Source: §H.1 · p. 33

H.2 Stepwise residual refinement on a fixed held-out real edge mask

The fixed-edge-mask analysis tracks first-order structural refinement against held-out real edges during denoising. Across additional held-out scans, MAGNET more consistently preserves global edge geometry, particularly on ADNI.

H.2 Stepwise residual refinement on a fixed held-out real edge mask

  • The fixed held-out real edge mask uses the top real class-mean edges, with generated-minus-real residuals compared using the same mask and color scale.Keeping the mask and scale fixed allows direct comparisons without threshold drift.Source: §H.2 · pp. 33–34
  • The masked-edge residual view measures first-order structural refinement, not full-distribution fidelity.The fixed real-defined mask makes masked-edge MAE a faithful proxy for the residual heatmaps.Source: §H.2 · p. 35
  • Across additional held-out scans, MAGNET more consistently preserves leading cross-hemispheric and frontal-posterior structure while maintaining lower or competitive Δ values.ADNI shows the clearest separation: DiffeoGauss oversmooths, TriangCFM often collapses toward a narrow core, and DiffeoCFM more frequently distorts global arrangement.Source: §H.2 · pp. 35–36, Figure 11 · p. 36

I Broader Impacts

MAGNET’s class-conditional connectome synthesis is framed as relevant to data-scarce clinical research and broader manifold-generation settings. The paper also flags risks that require validation before sensitive deployment.

I Broader Impacts

  • Geometrically valid, class-conditional connectomes may support data-scarce clinical research through augmentation, underrepresented-group synthesis, multi-site studies, and privacy-preserving sharing.The paper argues that subtype conditioning avoids unrealistic averaged samples from binary-supervised generators.Source: I Broader Impacts · p. 36
  • Class-conditional manifold awareness may matter beyond neuroimaging when nonlinear-manifold outputs must represent diverse subpopulations, including in molecular generation, materials science, and medical imaging.The paper presents MAGNET as a transferable framework for such settings.Source: I Broader Impacts · pp. 36–37
  • Synthetic connectomes may amplify source-data demographic biases, and discovered subtypes are statistical rather than clinically validated.The paper also identifies possible misuse of realistic synthetic data and calls for careful validation before sensitive deployment.Source: I Broader Impacts · p. 37

NeurIPS Paper Checklist

  • The checklist reports that experiments use 10 disjoint train/test splits and that empirical tables report standard deviations across 10 disjoint train/validation splits.It also states that wall-clock sampling times and hardware details are reported.Source: NeurIPS Paper Checklist · pp. 38–39

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