Spatial Gene Expression Prediction as Field Reconstruction from Histology

Spatial transcriptomics links gene expression to tissue morphology, but sequencing-based assays remain too costly and labor-intensive for routine profiling at scale. This has motivated a growing line of work on inferring spatial expression from standard hematoxylin-and-eosin (H&E) histology. Current methods, however, remain largely tied to assay-indexed prediction: they estimate expression at measured locations, with spatial context primarily used to inform predictions defined at those locations. This view is misaligned with how molecular signal is organized in tissue. Gene expression is not a set of isolated measurements, but a morphology-conditioned expression field shaped by regional tissue structure and resolved through local transcriptional variation. We formulate histology-based spatial gene expression prediction as *field reconstruction*. **Carta** reconstructs a morphology-conditioned expression field over the measured spatial coordinates of a spatial transcriptomics assay. It first estimates regional expression states from histology and then refines local expression by propagating information across nearby measured locations. To move beyond losses evaluated independently at sampled coordinates, Carta uses a bidirectional conditional transport objective that shapes the distributional structure of the reconstructed expression field across the spatial hierarchy. Across **16** organ-specific prediction tasks — **10** based on HEST-1k and **6** constructed from STImage-1K4M — Carta improves average PCC by **12.9** and **2.3** absolute PCC points over the UNI pathology foundation model baseline and the strongest baseline. It is particularly effective for sparse genes and spatially localized expression patterns, whose weak but structured variations can be under-represented by coordinate-level regression. These results show that morphology-conditioned field reconstruction provides a principled formulation for spatial expression prediction when direct molecular profiling is impractical.