Computer graphics cameras lack the finite depth of field (DOF) present in real world ones. This results in all objects being rendered sharp regardless of their depth, reducing the realism of the scene. On top of that, real-world DOF provides a depth cue, that helps the human visual system decode the elements of a scene. Several methods have been proposed to render images with finite DOF, but these have always implied an important trade-off between speed and accuracy. We introduce a novel anisotropic diffusion partial differential equation (PDE) that is applied to the 2D image of the scene rendered with a pin-hole camera. In this PDE, the amount of blurring on the 2D image depends on the depth information of the 3D scene, present in the Z-buffer. This equation is well posed, has existence and uniqueness results, and it is a good approximation of the optical phenomenon, without the visual artifacts and depth inconsistencies present in other approaches. Because both inputs to our algorithm are present at the graphics card at every moment, we can run the processing entirely in the GPU. This fact, coupled with the particular numerical scheme chosen for our PDE, allows for real-time rendering using a programmable graphics card.