The turbulent diapycnal mixing in the ocean is currently obtained from microstructure and finestructure measurements, dye experiments, and inverse models. This study presents a new method that infers the diapycnal mixing from low-resolution numerical calculations of the World Ocean whose temperatures and salinities are restored to the climatology. At the difference of robust general circulation ocean models, diapycnal diffusion is not prescribed but inferred. At steady state the buoyancy equation shows an equilibrium between the large-scale diapycnal advection and the restoring terms that take the place of the divergence of eddy buoyancy fluxes. The geography of the diapycnal flow reveals a strong regional variability of water mass transformations. Positive values of the diapycnal flow indicate an erosion of a deep-water mass and negative values indicate a creation. When the diapycnal flow is upward, a diffusion law can be fitted in the vertical and the diapycnal eddy diffusivity is obtained throughout the water column. The basin averages of diapycnal diffusivities are small in the first 1500 m [O(10(-5)) m(2) s(-1)] and increase downward with bottom values of about 2.5 x 10(-4) m(2) s(-1) in all ocean basins, with the exception of the Southern Ocean (50 degrees-30 degrees S), where they reach 12 x 10(-4) m(2) s(-1). This study confirms the small diffusivity in the thermocline and the robustness of the higher canonical Munk's value in the abyssal ocean. It indicates that the upward dianeutral transport in the Atlantic mostly takes place in the abyss and the upper ocean, supporting the quasi-adiabatic character of the middepth overturning.