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    <a class="brand" href="#top" aria-label="MAGNET home">MAGNET<span>.</span></a>
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      <a href="#abstract">Abstract</a>
      <a href="#overview">Method</a>
      <a href="#results">Results</a>
      <a href="https://doi.org/10.48550/arXiv.2610.17014" target="_blank" rel="noopener noreferrer">Paper</a>
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    <section class="hero" id="top" aria-labelledby="paper-title">
      <p class="venue">Accepted at NeurIPS 2026</p>
      <h1 id="paper-title">MAGNET: Manifold-Aware Graph Diffusion Network for Functional Brain Connectome Generation</h1>
      <p class="authors">
        <span><a href="https://protyayofficial.github.io/" target="_blank" rel="noopener noreferrer">Protyay Dey</a><sup>*</sup><sup>1</sup></span>
        <span><a href="https://ayushroy2001.github.io/" target="_blank" rel="noopener noreferrer">Ayush Roy</a><sup>*</sup><sup>1</sup></span>
        <span><a href="https://sites.google.com/view/hyunacho/home?pli=1&amp;authuser=0" target="_blank" rel="noopener noreferrer">Hyuna Cho</a><sup>2</sup></span>
        <span><a href="https://wwplato.github.io/" target="_blank" rel="noopener noreferrer">Won Hwa Kim</a><sup>3</sup></span>
        <span><a href="https://vlokhande-ub.github.io/" target="_blank" rel="noopener noreferrer">Vishnu Suresh Lokhane</a><sup>1</sup></span>
      </p>
      <p class="contribution"><sup>*</sup> Equal contribution</p>
      <p class="affiliations"><sup>1</sup> University at Buffalo, SUNY &nbsp;&middot;&nbsp; <sup>2</sup> National Institutes of Health, United States &nbsp;&middot;&nbsp; <sup>3</sup> POSTECH, South Korea</p>
      <p class="hero-summary">Valid correlation geometry is only the beginning. MAGNET generates class-conditional functional connectomes while preserving finer clinical structure.</p>
      <div class="hero-actions">
        <a class="button button-primary" href="https://doi.org/10.48550/arXiv.2610.17014" target="_blank" rel="noopener noreferrer">Read the paper <span aria-hidden="true">&nearr;</span></a>
        <a class="button button-primary" href="https://github.com/protyayofficial/MAGNET" target="_blank" rel="noopener noreferrer">Code &amp; reproduction <span aria-hidden="true">&nearr;</span></a>
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    <section class="abstract-section wrap" id="abstract" aria-labelledby="abstract-title">
      <p class="eyebrow">Abstract</p>
      <h2 id="abstract-title">Recovering class-conditional geometry in functional connectomes.</h2>
      <p>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&nbsp;settings.</p>
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    <section class="overview wrap" id="overview" aria-labelledby="overview-title">
      <div class="section-heading">
        <div><p class="eyebrow">The approach</p><h2 id="overview-title">Built around connectome geometry.</h2></div>
        <p>MAGNET treats a connectome as a structured point on the correlation-matrix manifold. A normalized-Cholesky coordinate preserves this geometry before ROI-level graph denoising, class-anchored conditioning, an amortized structural bridge, and relevance-preserving corruption shape the diffusion process.</p>
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      <div class="method-detail">
        <p>For a correlation matrix <i>C</i>, MAGNET writes <i>C = LL<sup>T</sup></i> and removes the diagonal scale from <i>L</i> before diffusing only through its strict lower triangle. With 39 MSDL regions this gives 741 latent coordinates. Decoding reconstructs the unit-lower-triangular factor, forms its Gram matrix, and renormalizes the diagonal, yielding a symmetric positive-definite correlation matrix with unit diagonal by construction.</p>
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      <a class="image-link architecture" href="docs/assets/arch.png" target="_blank" rel="noopener noreferrer" aria-label="Open the full-resolution MAGNET architecture image">
        <img src="docs/assets/arch.png" alt="MAGNET architecture showing correlation-matrix encoding, class-anchored conditioning, structural bridge, graph transformer denoising, and valid correlation decoding" width="1961" height="802">
        <span class="image-action">View full size <span aria-hidden="true">&nearr;</span></span>
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      <div class="highlights" aria-label="Key findings">
        <div><strong>6</strong><span>sampling steps</span></div>
        <div><strong>7-21%</strong><span>improvement in class-conditional &alpha;,&beta;-F1 across three cohorts</span></div>
        <div><strong>30%+</strong><span>improvement in zero-shot subclass covariance alignment</span></div>
      </div>
    </section>

    <section class="results" id="results" aria-labelledby="results-title">
      <div class="wrap">
        <div class="section-heading">
          <div><p class="eyebrow">The evidence</p><h2 id="results-title">Structure beyond validity.</h2></div>
          <p>Across ABIDE, ADNI, and OASIS-3, MAGNET is evaluated for class-conditional fidelity and preservation of finer connectome structure.</p>
        </div>
        <div class="visual-grid">
          <article class="visual-card">
            <a class="image-link visual-preview" href="docs/assets/multidataset_surface_similarity.png" target="_blank" rel="noopener noreferrer" aria-label="Open the full-resolution cortical hub mismatch image">
              <img src="docs/assets/multidataset_surface_similarity.png" alt="Cortical hub mismatch across ABIDE, ADNI, and OASIS-3" loading="lazy" width="1480" height="633">
              <span class="image-action">View full size <span aria-hidden="true">&nearr;</span></span>
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            <div class="visual-copy"><h3>Cortical hub alignment</h3><p>Spatial patterns across three independent cohorts.</p></div>
          </article>
          <article class="visual-card">
            <a class="image-link visual-preview samples-preview" href="docs/assets/all_datasets_split_0_class_1_sample_connectome_grid.png" target="_blank" rel="noopener noreferrer" aria-label="Open the full-resolution connectome samples image">
              <img src="docs/assets/all_datasets_split_0_class_1_sample_connectome_grid.png" alt="Real and generated functional connectomes across ABIDE, ADNI, and OASIS-3" loading="lazy" width="4533" height="4718">
              <span class="image-action">View full size <span aria-hidden="true">&nearr;</span></span>
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            <div class="visual-copy"><h3>Connectome samples</h3><p>Real and generated connectivity patterns, shown together.</p></div>
          </article>
        </div>
      </div>
    </section>

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      <a class="button button-primary" href="https://github.com/protyayofficial/MAGNET" target="_blank" rel="noopener noreferrer">Explore the code <span aria-hidden="true">&nearr;</span></a>
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