提出首个考虑染色非高斯特性的联邦域泛化方法，提升病理图像跨机构分析的鲁棒性。

Robust whole-slide image (WSI) analysis under strict data-governance remains challenging due to substantial cross-institutional stain heterogeneity. Domain generalization (DG) mitigates these shifts but typically requires centralized data, conflicting with privacy regulations. Federated learning (FedL) provides a decentralized alternative; however, existing FedL and federated DG (FedDG) approaches rely almost exclusively on low-order statistics, assuming Gaussian-like stain distributions. In contrast, real-world staining processes often produce asymmetric, heavy-tailed color distributions due to biochemical diffusion and scanner nonlinearity. Consequently, current methods fail to model the higher-order, non-Gaussian characteristics dominating real-world stain variability. To address this, we propose FedStain, a stain-aware FedDG framework explicitly incorporating higher-order stain moments--skewness and kurtosis--as compact statistical descriptors exchanged during federated optimization. These descriptors require no pixel-level data transmission, preserving strict privacy and communication efficiency, while enabling the global model to capture stain variability missed by low-order statistics. FedStain also employs a contrastive, cross-site parameter aggregation strategy to promote stain-invariant representations without relaxing data constraints. Extensive experiments on Camelyon17 and our new MvMidog-Fed benchmark show FedStain yields consistent improvements, outperforming state-of-the-art FedL, DG, and FedDG baselines by up to +3.9% absolute accuracy. To our knowledge, FedStain is the first FedDG approach to explicitly model higher-order stain statistics, enabling robust cross-institutional deployment in computational pathology.