Spatial omics technologies enable analysis of gene expression and interaction dynamics in relation to tissue structure and function. However, existing computational methods may not properly distinguish cellular intrinsic variability and intercellular interactions, and may thus fail to reliably capture spatial regulations. Here, we present Spatial Interaction Modeling using Variational Inference (SIMVI), an annotation-free deep learning framework that disentangles cell intrinsic and spatial-induced latent variables in spatial omics data with rigorous theoretical support. By this disentanglement, SIMVI enables estimation of spatial effects at a single-cell resolution, and empowers various downstream analyses. We demonstrate the superior performance of SIMVI across datasets from diverse platforms and tissues. SIMVI illuminates the cyclical spatial dynamics of germinal center B cells in human tonsil. Applying SIMVI to multiome melanoma data reveals potential tumor epigenetic reprogramming states. On our newly-collected cohort-level CosMx melanoma data, SIMVI uncovers space-and-outcome-dependent macrophage states and cellular communication machinery in tumor microenvironments.