We study diffusion on topologically linear fractal structures under the influence of a uniform external field. Due to the fractal nature of the chain, the uniform field acts on a random walker like random correlated (local) fields in a one-dimensional chain. We find that the mean square displacement of the walker is universal and depends logarithmically on time t as ⟨r²⟩ ∼ ln²t, independent of the fractal dimension of the chain.