The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, $$\theta $$ θ and controlled by two control parameters: (i) $$\epsilon $$ ϵ , controlling the nonlinearity of the system, particularly a transition from integrable for $$\epsilon =0$$ ϵ = 0 to non-integrable for $$\epsilon \ne 0$$ ϵ ≠ 0 and; (ii) $$\gamma $$ γ denoting the power of the action in the equation defining the angle. For $$\epsilon \ne 0$$ ϵ ≠ 0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.