Generative Myopia: Why Diffusion Models Fail at Structure

TL;DR

This paper identifies why diffusion models struggle with structural features in graphs due to frequency bias and gradient starvation, and proposes a spectral weighting method to improve their ability to preserve critical sparse structures.

Contribution

The paper introduces Spectrally-Weighted Diffusion, a novel approach that incorporates spectral priors to overcome generative myopia in graph diffusion models.

Findings

Eliminates structural myopia in graph diffusion models.

Achieves 100% connectivity on challenging benchmarks.

Matches the performance of an optimal spectral oracle.

Abstract

Graph Diffusion Models (GDMs) optimize for statistical likelihood, implicitly acting as \textbf{frequency filters} that favor abundant substructures over spectrally critical ones. We term this phenomenon \textbf{Generative 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 \textbf{Gradient Starvation}: the optimization landscape itself suppresses rare structural signals, rendering them unlearnable regardless of model capacity. To resolve this, we introduce \textbf{Spectrally-Weighted 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 \textbf{100\% connectivity} on adversarial benchmarks where standard diffusion fails completely (0\%).