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The unique properties of organic semiconductors, such as flexibility and lightness, are increasingly important for information displays, lighting and energy generation. But organics suffer from both static and dynamic disorder, and this can lead to variable-range carrier hopping, which results in notoriously poor electrical properties, with low electron and hole mobilities and correspondingly short charge-diffusion lengths of less than a micrometre. Here we demonstrate a photoactive (light-responsive) organic heterostructure comprising a thin fullerene channel sandwiched between an electron-blocking layer and a blended donor:C70 fullerene heterojunction that generates charges by dissociating excitons. Centimetre-scale diffusion of electrons is observed in the fullerene channel, and this can be fitted with a simple electron diffusion model. Our experiments enable the direct measurement of charge diffusivity in organic semiconductors, which is as high as 0.83 ± 0.07 square centimetres per second in a C60 channel at room temperature. The high diffusivity of the fullerene combined with the extraordinarily long charge-recombination time yields diffusion lengths of more than 3.5 centimetres, orders of magnitude larger than expected for an organic system.