发表机构
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对图信号谱能量不均导致扩散模型噪声范围过大的问题，提出GRCD方法，通过模式依赖时钟实现SNR均衡，在五个数据集上显著降低aMMD并提升采样效率。
AI 中文摘要
扩散模型通过逆转一个通常趋近于简单高斯先验的前向破坏过程来生成数据。近期工作将该框架扩展至固定图上的信号，例如路网交通和传感器网络测量。许多图信号的谱能量分布不均匀，而各向同性破坏为每个图频率模式添加相同的条件噪声方差。将所有模式驱动至接近零的终端信噪比（SNR）需要强破坏，这增加了在固定采样预算下必须覆盖的噪声范围。我们提出了图残差共轭扩散（GRCD），该方法将图热扩散的共享时钟替换为依赖于模式的时钟，使每个图傅里叶模式具有相同的条件SNR。GRCD在训练分割上拟合一个零均值图谱高斯参考，并在有限终端SNR处停止，此时传播的参考仍携带拟合的谱方差。高斯分量在概率流ODE中具有精确的逐模式传播器，因此采样可解析地推进该分量，仅需数值积分学习的残差分数。我们在五个设置（METR-LA交通、Molene天气和三个随机块模型）上，在匹配协议下与七个比较方法（图感知扩散（GAD）、EDM（图主干）、白化分数扩散（WSD）的两种改编以及三个预条件控制）进行对比评估。在四次函数评估（NFEs）下，GRCD在所有五个设置上将平均最大均值差异（aMMD）相对于最佳比较方法降低了22至36倍，在METR-LA上达到0.054，并以比达到该目标的最便宜比较方法少87%的采样墙钟时间清除了0.1的aMMD目标。拟合终端参考在有限终端SNR下将aMMD降低了2.7至7.3倍，而在接近零时该因子缩小至1.00至1.01。
英文摘要
Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals supported on fixed graphs, e.g., road-network traffic and sensor-network measurements. Many graph signals have nonuniform spectral energy, whereas isotropic corruption adds the same conditional noise variance to every graph-frequency mode. Driving all modes to near-zero terminal signal-to-noise ratio (SNR) requires strong corruption, which increases the noise range that must be covered under a fixed sampling budget. We introduce Graph Residual Conjugate Diffusion (GRCD), which replaces the shared clock of graph heat diffusion with a mode-dependent clock that gives every graph-Fourier mode the same conditional SNR. GRCD fits a zero-mean graph-spectral Gaussian reference on the training split and stops at a finite terminal SNR at which the propagated reference still carries the fitted spectral variances. The Gaussian component has an exact modewise propagator in the probability-flow ODE, so sampling advances it analytically and integrates only the learned residual score numerically. We evaluate GRCD on five settings (METR-LA traffic, Molene weather, and three stochastic block models) against seven comparators under a matched protocol: Graph-Aware Diffusion (GAD), EDM (graph backbone), two adaptations of Whitened Score Diffusion (WSD), and three preconditioning controls. At four function evaluations (NFEs), GRCD lowers averaged maximum mean discrepancy (aMMD) by 22 to 36 times over the best comparator on all five settings, reaching 0.054 on METR-LA, where it clears an aMMD 0.1 target with 87% less sampling wall-clock time than the cheapest comparator that reaches it. Fitting the terminal reference reduces aMMD by 2.7 to 7.3 times at finite terminal SNR, while the factors shrink to 1.00 to 1.01 near zero.
Comments23 pages, 2 figures
