<p>Cell-cell communication is fundamental for coordinating cellular activities, maintaining tissue homeostasis, and supporting physiological functions. This complex process is primarily mediated by ligand-receptor interactions, in which ligands bind to cognate receptors to trigger downstream signaling. Conventional approaches for inferring cellular communication from single-cell transcriptomics are constrained by group-level resolution and spatial false-positive artifacts. The advent of spatial transcriptomics technologies has overcome these limitations by enabling spatially resolved analyses of communication events. In this study, we present SCILD (Spatial Cellular communication Inference with Ligand Diffusion and transport model), an interpretable optimization-based framework that infers spatial cellular communication at single-cell resolution from spatial transcriptomics data. SCILD integrates ligand diffusion, competitive ligand-receptor binding, and concentration decay into a unified optimization model, conceptualized as a cargo transport system with potential losses. By further incorporating neural network modeling with in silico perturbation, SCILD can predict downstream target genes of ligand-receptor interactions. Comprehensive validations demonstrate that SCILD accurately captures competitive communication dynamics at single-cell level, identifies biologically meaningful ligand-receptor markers that govern domain-specific signaling, resolves subdomain-specific communication patterns, and robustly predicts target genes supported by external databases. Collectively, these results establish SCILD as a versatile and powerful tool for advancing spatial cellular communication research.</p>