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Up to now, diffusive load balancing schemes have only been developed for homogeneous networks. We generalize existing diffusion schemes, in order to deal with heterogeneous networks. In these networks, every processor can have arbitrary computing power, and the load has to be balanced proportionally to these weights. The balancing flow that is calculated by the schemes for homogeneous networks is minimal with regard to the l2-norm and we prove this to hold true for the generalized schemes, too. By means of a number of experiments we demonstrate the usability of the generalized schemes on heterogeneous networks.