The trapping model for the annihilation rate of positrons implanted in solids has been combined with a diffusion model for the spatial motion of the implanted positrons prior to annihilation. Results are given for a simple system having traps only at the surface of a sample and allowing no detrapping, and for a general case where both effects are included. Numerical results are given for the example of positrons trapping in an image-potential well (as well as forming positronium) at a surface.