Finding correlations in spatial gene expression is fundamental in spatial transcriptomics, as co-expressed genes within a tissue are linked by regulation, function, pathway, or cell type. Yet, sparsity and noise in spatial transcriptomics data pose significant analytical challenges. Here, we introduce Smoothie, a method that denoises spatial transcriptomics data with Gaussian smoothing and constructs and integrates genome-wide co-expression networks. Utilizing implicit and explicit parallelization, Smoothie scales to datasets exceeding 100 million spatially resolved spots with fast run times and low memory usage. We demonstrate how co-expression networks measured by Smoothie enable precise gene module detection, functional annotation of uncharacterized genes, linkage of gene expression to genome architecture, and multi-sample comparisons to assess stable or dynamic gene expression patterns across tissues, conditions, and time points. Overall, Smoothie provides a scalable and versatile framework for extracting deep biological insights from high-resolution spatial transcriptomics data.