In nature there are many systems which appear to exhibit some form of self-organization. Among these are forest fires, earthquakes, sandpiles, turbulent transport and even many aspects of society itself. Investigations into the similarity of the dynamics of such systems have been undertaken by using simple cellular automata models. A running sandpile Self-Organized Criticality (SOC) model for turbulent transport in magnetically confined plasmas has been used explain some of the observed features of the transport dynamics in these plasmas. These models have produced a remarkable amount of insight into the dynamics of such systems. However, most real systems have some diffusive like process in addition to the transport events in our simple models. Therefore we add such a mechanism and have discovered a rich new world of dynamics. Some of the basic features of SOC systems will first be reviewed. Then, an extension of a sandpile model to include diffusion will be introduced, and the details of an observed dynamical transition (you have to come to the talk to learn what that is) will be explored. Finally, time permitting, some speculation on the implications for understanding the dynamics of real systems (plasma transport and earthquakes) the context of a diffusive SOC system will be discussed.