Understanding the relevant permeability properties of ultrafiltration membranes is facilitated by using materials and procedures that allow a high degree of control on morphology and chemical composition. Here we present the first study on diffusion permeability through gyroid nanoporous cross-linked 1,2-polybutadiene (1,2-PB) membranes with uniform pores that, if needed, can be rendered hydrophilic. The gyroid porosity has the advantage of isotropic percolation with no need for structure prealignment. Closed (skin) or opened (nonskin) outer surface can be simply realized by altering the interface energy in the process of membrane fabrication. The morphology of the membranes' outer surface was investigated by scanning electron microscopy, contact angle, and X-ray photoelectron spectroscopy. The effective diffusion coefficient of glucose decreases from nonskin, to one-sided skin to two-sided skin membranes, much faster than expected by a naive resistance-in-series model; the flux through the two-sided skin membranes even increases with the membrane thickness. We propose a model that captures the physics behind the observed phenomena, as confirmed by flow visualization experiments. The chemistry of 1,2-PB nanoporous membranes can be controlled, for example, by hydrophilic patterning of the originally hydrophobic membranes, which allows for different active porosity toward aqueous solutions and, therefore, different permeability. The membrane selectivity is evaluated by comparing the effective diffusion coefficients of a series of antibiotics, proteins, and other biomolecules; solute permeation is discussed in terms of hindered diffusion. The combination of uniform bulk morphology, isotropically percolating porosity, controlled surface chemistry, and tunable permeability is distinctive for the presented gyroid nanoporous membranes.