Although covalent organic frameworks (COFs) demonstrate notable potential for developing advanced separation membranes, contemporary COF membranes still lack controlled stacking and highly efficient sieving. Here, Turing-architecture COF membranes were constructed by engineering a reaction-diffusion assembly process via heterogeneous nucleation synthesis with tannic acid (TA). TA covalently binds with amine monomers to form a composite precursor with increased reactivity and decreased diffusivity. This altered the pathway of Schiff base reactions with aldehyde monomers, fulfilling suitable reaction-diffusion conditions, and ultimately formed the labyrinthine stripe or spot-patterned Turing COF film with controlled stacking and uniform pore structure. This endows our COF membrane with highly efficient molecule sieving ability for organic solvent nanofiltration while exhibiting a flux that is 621% greater than that of commercial membranes. Thus, this study provides a paradigm for the in situ synthesis of highly efficient COF membranes for diversely sustainable separations.