This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models which seek to explain the diffusion of an epidemic in a network. The Susceptible-Infected-Recovered (SIR) model is a classic example, proposed nearly a century ago [2]. The SIR model remains a cornerstone for the forecasting of epidemics. The so-called Bass model [1] remains a basic building block in forecasting consumer adoption of new products and services. The durability of these models arises from the fact that they have shown an excellent fit to data, in numerous studies spanning both the epidemiology and marketing literatures. Somewhat paradoxically, using these same models as reliable forecasting tools presents a challenge.