CLEAR-ST: Physics-informed probabilistic decontamination of spatial transcriptomics by modeling mRNA lateral diffusion

Spatial transcriptomics is a rapidly evolving technology that allows for the measurement of gene expression in a spatially resolved manner. However, one technical problem that occurs for many sequencing-based spatial transcriptomics platforms is the presence of mRNA lateral diffusion, where mRNA from one spot can bind to probes in another spot, leading to contamination and inaccurate gene expression measurements. In Visium-like assays, this artifact is often visible as structured out-of-tissue signal and boundary-associated expression halos, yet its magnitude, spatial decay, and directional bias vary substantially across samples. Here, we present CLEAR-ST, a physics-informed probabilistic framework for correcting diffusion-like contamination in spatial transcriptomics data. CLEAR-ST infers a latent clean expression field using a denoising autoencoder and links it to the observed counts through a graph-Laplacian forward contamination model with learnable diffusion parameters, finally evaluated with a selectable count likelihood. We first conducted a comprehensive comparison between 10X official and independently generated Visium samples, demonstrating that out-of-tissue count profiles are highly related to nearby in-tissue expression, more concentrated near tissue boundaries, and diffusion directions across genes are likely coherent. Across real samples with varying contamination burden, CLEAR-ST improved spatial domain recovery, increased gene-level spatial autocorrelation, and enhanced the biological specificity of downstream analyses such as marker gene discovery, pathway identification and cell type deconvolution. Compared to benchmark methods, CLEAR-ST showed consistent gains in clustering quality and concordance with manual annotations. Together, CLEAR-ST provides an interpretable and practical approach for diffusion-aware correction of capture-based spatial transcriptomics data.