We found stationary intensity profiles of photorefractive screening solitons in the presence of the diffusion processes. We show that these solitons are stable and in a certain range of parameters they propagate with negligible radiation losses along exactly parabolic trajectories. We studied the collision of screening solitons using numerical simulations. We found that even a small contribution of the diffusion effect leads to strong energy exchange between the colliding photorefractive solitons. 1996 The American Physical Society.