This paper proposes the Average Diffusion (ADF) method for solving the load balancing problem. It is shown that a sufficient and necessary condition for the ADF method to converge to the uniform distribution of loads is the induced network of processors to be d-regular, connected and not bipartite. Next, we proceed and apply Fourier analysis determining the convergence factor γ in terms of the diffusion parameters c _ij (weighted case) when the network of processors is a ring and 2D-torus. It is shown that c _ij = 1/2 and c _ij ∈ (0, 1/2) when the network is a ring and 2D-torus, respectively, thus solving partially the open problem which concerns the determination of the diffusion parameters c _ij.