The solution to the non–forward BFKL equation in the Leading Logarithmic approximation is expressed in terms of a sum of iterations of its kernel directly in transverse momentum and rapidity space. Several studies of the non–forward solution are performed both at the level of the gluon Green’s function and for a toy cross–section, including an analysis of the diffusion properties as found in this approach. The method developed in this paper allows for a direct inspection of the momenta in the BFKL ladder, and can be applied to solving the non–forward BFKL equation to next–to–leading logarithmic accuracy, when the corresponding kernel is available.