molecular transport and interaction are of fundamental importance in biology and medicine. the spatiotemporal diffusion map can reflect the regulation of molecular interactions and their intracellular functions. to construction subcellular diffusion maps based on bio-imaging data, we explore a general optimization framework with diffusion equation constraints (opt-pde) and finite element discretization to enable the solution of a spatiotemporal and anisotropic diffusion map. we characterize the wellposedness and convergence property of the opt-pde solver and demonstrate its applicability in re-covering heterogeneous and anisotropic diffusion maps in bio-imaging. furthermore, to study molecular interactions based on live-cell imaging, we developed a correlative fret imaging microscopy (cfim) approach for the quantitatively analysis of subcellular coordination between the enzymatic activity and the structural focal adhesion (fa) dynamics. by cfim, we found that different fa subpopulations have distinct regulation mechanisms controlled by local kinase activity. therefore, our work highlights the importance of computational model-based analysis and its integration with bio-imaging.