Coarse-to-Fine Diffusion Transformers for Recovering Spatial EMT Programs from H&E Histology

Spatial transcriptomics measures gene expression in tissue context but remains costly, whereas hematoxylin-and-eosin (H\&E) histology is inexpensive and widely available in large-scale clinical archives. We investigate whether H\&E images can recover a fixed, biologically defined spatial gene program, rather than a cohort-specific set of highly variable genes, using a tumor-agnostic epithelial-mesenchymal transition (EMT) signature as a test case. We introduce \textbf{CFDiT}, a coarse-to-fine diffusion-transformer framework that encodes spatial inductive bias in its training targets. A graph-Tikhonov operator decomposes the expression profile of each training slide into a spatially smooth coarse field and a residual component. A first diffusion transformer predicts the coarse field from tissue morphology, and a second predicts the residual conditioned on the coarse prediction. Across prostate and breast cancer cohorts, under patient-disjoint evaluation with four random seeds, CFDiT achieves higher panel-wide correlation than all implemented baselines. We further partition the EMT panel into $44$ Gene Ontology sub-signatures and find that branch-level scores are recovered more reliably than individual-gene expression, with performance improving as branch size increases.