Abstract: Label-free virtual staining offers a compelling, non-destructive alternative to standard histopathology; however, its clinical adoption is hindered by the computational bottlenecks inherent to processing gigapixel Whole Slide Images (WSIs). Current deep learning approaches require patch-based inference to avoid memory constraints, which disrupts global tissue continuity and introduces tiling artifacts--displaying visible seams and color shifts. To address this, we introduce the Consistency Memory Bank (COMB), a novel label-free virtual staining framework that enforces spatial and channel consistency across tiles without memory bottlenecks. COMB decouples context storage from computation, utilizing a dynamic retrieval mechanism to fetch feature representations from adjacent tiles. This enables a retrieval-based context integration strategy that adopts local padding to resolve spatial discontinuities and neighbor-aware channel attention to stabilize statistical drift. Further optimized with a sliding window schedule to ensure minimal memory overhead, our method demonstrates superior performance over state-of-the-art baselines, achieving significant improvements in both perceptual fidelity and tiling consistency, while suggesting its downstream utility in tumor segmentation. Code is available at https://github.com/dou0000/COMB.