We suggest a new mesh free random walk method for solving boundary value problems in semi-infinite domains with mixed boundary conditions. The method is based on a probabilistic interpretation of the diffusion processes. Our simulations show that the suggested algorithm is extremely efficient for solving diffusion imaging problems, in particular, for calculating the defect contrast in cathodoluminescence (CL) and electron beam-induced current (EBIC) techniques. The method avoids to simulate the long diffusion trajectories. Instead, it exploits exact probability distributions of the first passage and survival probabilities.