Diffusion-sensitized magnetic resonance imaging provides information about the fibrous structure of the human brain. However, this information is not sufficient to reconstruct the underlying fiber network, because the nature of diffusion provides only conditional fiber densities. That is, it is possible to infer the percentage of bundles that pass a voxel with a certain direction, but the absolute number of fibers is inaccessible. In this work we propose a conservation equation for tensor fields that can infer this number up to a factor. Simulations on synthetic phantoms show that the approach is able to derive the densities correctly for various configurations. In-vivo results on 20 healthy volunteers are plausible and consistent, while a rigorous evaluation is difficult, because conclusive data from both MRI and histology remain elusive even on the most studied brain structures.