The authors study, within a renormalisation group scheme, two possible generalisations of a one-dimensional (1D) diffusion model with a hierarchy of energy barriers recently proposed. They consider the same 1D model plus a biasing term and a 2D version of it, In the first case they find, for a suitable value of the biasing force, a new transition in the long-time behaviour of the autocorrelation function. For the 2D model, through an approximate treatment, they obtain the corresponding anomalous exponent which characterises its relational behaviour.