We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151-164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.