Flocks of birds self-organize into V-formations when they need to travel long distances. It has been shown that this formation allows the birds to save energy, by taking advantage of the upwash generated by the neighboring birds. In this work we use a model for the upwash generated by a flying bird, and show that a flock of birds can self-organize into a V-formation if every bird were to process spatial and network information through an adaptive diffusive process. The diffusion algorithm requires the birds to obtain measurements of the upwash, and also to use information from neighboring birds. The result has interesting implications. First, a simple diffusion algorithm can account for self-organization in birds. The algorithm is fully distributed and runs in real time. Second, according to the model, that birds can self-organize based on the upwash generated by the other birds. Third, that some form of information sharing among birds is necessary to achieve flight formation. We also propose a modification to the algorithm that allows birds to organize into a U-formation, starting from a V-formation. We show that this type of formation leads to an equalization effect, where every bird in the flock observes approximately the same upwash.