Align as You Couple: Learning Spatial Resolved Inference from H&E Images with Mollified Flow Matching

Spatial resolved inference (SRI) is a critical technique in biomedical research, which aims to measure RNA sequence abundances by associating them with whole-tissue images at a fine-grained molecular scale. However, the extremely low throughput and distributional discrepancies involved pose significant challenges to cellular morphologies captured in hematoxylin and eosin (H&E) connection benchmarking, and existing SRI frameworks suffer from coverage gaps. In this paper, we propose MollFlow, a novel generative Mollified Flow matching model for spatial resolution inference, which is designed to learn the probabilistic dependency between the distributions of whole-slide images and expression profiles. We innovatively reframe the anchors of flow matching as a sequential informative prior derived from whole-slide images rather than isotropic Gaussian noise. During inference, MollFlow progressively refines the prior trajectory, ultimately converging to biologically plausible inferences. For the challenging coupling, which requires enabling intermediate states to explore pathologically aligned subspaces, we carry out a boundary mollified strategy to stabilize the velocity field, rather than being constrained by rigid trajectories. Endowed by this, our unique modulation generation perspective allows the model to retain coupling alignment for manifold incommensurability and prevent coverage gaps. Empirically, we find that MollFlow is capable of accurately inferring gene expression while exhibiting excellent performance in a variety of application scenarios.