GAMMI: graph-guided contrastive and adversarial integration of single-cell and spatial multi-omics data.

Integrating single-cell and spatial multi-omics data is essential for resolving cellular identity, regulatory programs and tissue organization, yet remains challenging under realistic experimental designs. In practice, data are often incomplete, unpaired and partially overlapping across batches and platforms, resulting in mosaic settings where missingness, batch effects and limited correspondence are tightly coupled. Existing methods typically rely on shared cells, explicit anchors or post hoc mapping, and can become unstable as overlap diminishes or spatial structure is not explicitly modeled. Here we present GAMMI (Graph-guided Adversarial Mosaic Multi-omics Integration), a unified graph learning framework for mosaic integration of heterogeneous single-cell and spatial multi-omics data. Rather than performing direct cell or sample alignment, GAMMI learns biologically meaningful relational structure by jointly embedding cells and molecular features in a shared latent space using heterogeneous graphs that encode cell-feature, feature-feature and spatial adjacency relationships. An edge-based contrastive objective with missingness-aware negative sampling avoids false-negative supervision under unobserved modalities, while adversarial domain adaptation suppresses batch-associated variation at the embedding level. Spatial data are incorporated as structurally informative constraints during learning, enabling systematic enrichment of molecular representations across spatial locations. Across diverse mosaic single-cell benchmarks and spatial datasets, GAMMI consistently outperforms state-of-the-art methods in biological conservation, batch correction and spatial reconstruction, including in low-overlap and fully unpaired regimes.