Vector fields are normally the result of computer simulations, or measurements, done in a number of scientific fields. This can be in fluid dynamics, meteorology, medicine, climate modeling and oil exploration, just to mention a few. To be able to understand and interpret these data, we normally need to transform them into images. A good image will hopefully also help us in obtaining new insight into the underlying physics. To display an image of a 2D vector fields is fairly simple. However, meaningful images of 3D fields are much more challenging to produce, as cluttering and occlusion often obscure important details. In this work we present a techniques that solve some of these issues, and produce high quality images and animations of 2D and 3D vector fields. This is done by solving a partial differential equation (PDE) for anisotropic diffusion, and displaying the results in modern Volume Rendering software.