GBFlow: Grouping Belief-Guided Dual Normalizing Flows for Accurate Spatial Domain Delineation

Abstract

Existing spatial domain identification methods primarily use graph neural networks to model spatial and transcriptional relationships. However, their performance is highly sensitive to noisy affinity graphs. Moreover, graph autoencoders tend to over-constrain latent representations, which limits their ability to capture global variability in spatial multi-omics data. To overcome these issues, we propose a dual-flow latent refinement framework that simultaneously integrates structure-aware and structure-free transformations. Specifically, a graph normalizing flow is employed to enforce relational consistency, while a parallel vanilla normalizing flow preserves global distributional flexibility. Features learned by the two flows are then adaptively fused to obtain a robust and unified latent representations. In addition, we introduce a grouping belief-based affinity refinement strategy to suppress unreliable connections and strengthen confident neighborhood relationships, which provides a more stable structural prior for representation learning. Extensive experiments on multiple spatial multi-omics datasets show that the proposed method consistently outperforms state-of-the-art approaches and achieves more accurate and robust spatial domain identification. The supplementary material is publicly available at https://github.com/LiangSDNULab/GBFlow.