We demonstrate experimentally that optical wavefront shaping increases light coupling into the fundamental diffusion mode of a scattering medium. The total energy density inside a scattering medium of zinc oxide nanoparticles was probed by exciting fluorescent spheres that were randomly positioned in the medium and collecting the fluorescent power. We optimized the incident wavefront to obtain a bright focus at the back surface of the sample and found that the concomitant fluorescent power is enhanced compared to a non-optimized incident wavefront. The observed enhancement increases with sample thickness. Based on diffusion theory, we derive a model wherein the distribution of the energy density of wavefront-shaped light is dominated by the fundamental diffusion mode. Our model agrees remarkably well with our experiments, notably since the model has no freely adjustable parameters.