Generative Myopia: Why Diffusion Models Fail at Structure

Graph Diffusion Models (GDMs) optimize for statistical likelihood, implicitly acting as $\mathbf{\text{frequency}}\mathbf{\text{filters}}$ that favor abundant substructures over spectrally critical ones. We term this phenomenon $\mathbf{\text{Generative}}\mathbf{\text{Myopia}}$. In combinatorial tasks like graph sparsification, this leads to the catastrophic removal of ``rare bridges,‘’ edges that are structurally mandatory ($R_{\text{eff}}\approx 1$) but statistically scarce. We prove theoretically and empirically that this failure is driven by $\mathbf{\text{Gradient}}\mathbf{\text{Starvation}}$: the optimization landscape itself suppresses rare structural signals, rendering them unlearnable regardless of model capacity. To resolve this, we introduce $\mathbf{\text{Spectrally-Weighted}}\mathbf{\text{Diffusion}}$, which re-aligns the variational objective using Effective Resistance. We demonstrate that spectral priors can be amortized into the training phase with zero inference overhead. Our method eliminates myopia, matching the performance of an optimal Spectral Oracle and achieving $\mathbf{\text{100\%}}\mathbf{\text{connectivity}}$ on adversarial benchmarks where standard diffusion fails completely (0%).