Carbon-based semiconductors such as conjugated organic polymers are of potential use in the development of spintronic devices and spin-based information processing. In particular, these materials offer a low spin–orbit coupling strength due to their relatively light constituent chemical elements, which should, in principle, favour long spin diffusion lengths. However, organic polymers are relatively disordered materials and typically have a carrier mobility that is orders of magnitude lower than crystalline inorganic materials. As a result, small spin diffusion lengths of around 50 nm have typically been measured using vertical organic spin valves. Here we report measuring spin diffusion lengths in doped conjugated polymers using a lateral spin transport device architecture, which is based on spin pumping injection and inverse spin Hall detection. The approach suggests that long spin diffusion lengths of more than 1 micron and fast spin transit times of around 10 ns are possible in conjugated polymer systems when they have a sufficiently high spin density (around 10^20 cm-3). We explain these results in terms of an exchange-based spin diffusion regime in which the exchange interactions decouple spin and charge transport.