Spatial omics technologies enable the 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 capture spatial regulations for further biological discoveries. Here, we present Spatial Interaction Modeling using Variational Inference (SIMVI), an annotation-free framework that disentangles cell intrinsic and spatial-induced latent variables for modeling gene expression in spatial omics data. We derive theoretical support for SIMVI in disentangling intrinsic and spatial-induced variations. By this disentanglement, SIMVI enables estimation of spatial effects (SE) at a single-cell resolution, and opens up various opportunities for novel downstream analyses. To demonstrate the potential of SIMVI, we applied SIMVI to spatial omics data from diverse platforms and tissues (MERFISH human cortex, Slide-seqv2 mouse hippocampus, Slide-tags human tonsil, spatial multiome human melanoma, cohort-level CosMx melanoma). In all tested datasets, SIMVI effectively disentangles variations and infers accurate spatial effects compared with alternative methods. Moreover, on these datasets, SIMVI uniquely uncovers complex spatial regulations and dynamics of biological significance. In the human tonsil data, SIMVI illuminates the cyclical spatial dynamics of germinal center B cells during maturation. Applying SIMVI to both RNA and ATAC modalities of the multiome melanoma data reveals potential tumor epigenetic reprogramming states. Application of SIMVI on our newly-collected cohort-level CosMx melanoma dataset uncovers space-and-outcome-dependent macrophage states and the underlying cellular communication machinery in the tumor microenvironments.