这篇论文从理论上分析了图信号生成流模型的结构扰动稳定性，还给了个实用的正则化训练方法，在fMRI等真实数据上验证有效。
本文分析了由GNN参数化的连续归一化流模型在图信号生成中的稳定性。作者证明排列等变性在连续时间ODE及其数值近似中均保持。推导了显式的稳定性界限，量化图结构扰动对生成信号分布的影响。基于理论界限引入正则化流匹配策略，在训练中惩罚向量场的空间Lipschitz常数。在随机块模型合成信号和真实fMRI脑连接体信号上的实验表明，该方法对结构噪声更鲁棒且不牺牲输出质量。
Stability of Flow Models for Graph Signals
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.