We construct a diffusive, bi-stable cellular automata model to elucidate the physical mechanisms underlying observed edge localized mode (ELM) mitigation by supersonic molecular beam injection (SMBI). The extended cellular automata model reproduces key qualitative features of ELM mitigation experiments, most significantly the increase in frequency of grain ejection events (ELMs), and the decrease in the number of grains ejected by these transport events. The basic mechanism of mitigation is the triggering of small scale pedestal avalanches by additional grain injection directly into the H-mode pedestal. The small scale avalanches prevent the gradient from building-up to marginality throughout the pedestal, thus avoiding large scale transport events which span the full extent of that region. We explore different grain injection parameters to find an optimal SMBI scenario. We show that shallow SMBI deposition is sufficient for ELM mitigation.