Recent variational stereo approaches suffer from at least one of the following drawbacks: Either they use an isotropic disparity-driven smoothness term that ignores the directional information of the disparity field, or they apply anisotropic imagedriven regularisation that suffers from oversegmentation artifacts. As a remedy, we present a novel anisotropic disparity-driven approach for stereo vision. It is designed as a highly adaptive anisotropic diffusion-reaction equation that incorporates a diffusion process which has been used successfully for image denoising and inpainting. Its directional adaptation allows to better control the smoothing wrt the local structure of the disparity field. Experiments that compare our model to a recent isotropic variational method and a probabilistic graph cut approach demonstrate the superior quality of our approach. Moreover, a multigrid algorithm allows for moderate run times that do not depend on the disparity range.