MANGO: Flow Matching on the Multiplicative Geometry of Gene Expression for Spatial Transcriptomics Prediction from Histology

Predicting spatial molecular profiles from routine H&E images can extend spatial omics to large pathology cohorts, but existing methods commonly rely on Euclidean generative paths, fixed tissue graphs, and uniformly weighted gene objectives. These choices overlook the multiplicative geometry of nonnegative gene expression, prevent tissue neighborhoods from adapting to the evolving molecular state, and bias learning toward abundant genes. We propose MANGO, an expression-conditioned Riemannian graph flow for histology-based spatial-omics prediction. MANGO performs conditional flow matching on the multiplicative geometry of gene expression and predicts the clean expression endpoint, yielding closed-form geodesic corruption and geometry-preserving denoising. A dynamic multi-view graph Transformer jointly models spatial proximity, morphological similarity, and the current multiplicative expression state, and reconstructs the graph layer by layer. An expression-aware Riemannian objective further balances supervision across genes. Across 17 transcriptomics datasets spanning spot-level, Visium HD, and cell-level resolutions, MANGO ranks first on 10 and second on the remaining seven, while achieving the highest average PCC in all four evaluation groups. It also leads in four representative all-gene settings and reaches PCC values of 0.409 and 0.292 on spatial metabolomics and proteomics, surpassing the strongest baselines by 0.176 and 0.088, respectively. These results demonstrate that coupling expression-aware geometry with adaptive tissue structure enables accurate and resolution-robust spatial-omics inference from histology.