If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally distributed across trials, the starting point for the process is assumed to be uniformly distributed across trials, and the time taken by processes outside the diffusion process is assumed to be uniformly distributed. With the studies in this article, I explore the consequences of alternative assumptions about the distributions, using a wide range of parameter values. The model with the standard assumptions was fit to predictions generated with the alternative assumptions, and the results showed that the recovered parameter values matched the values used to generate the predictions with only a few exceptions. These occurred when parameter combinations were extreme and when a skewed distribution (exponential) of nondecision times was used. The conclusion is that the standard model is robust to moderate changes in the across-trial distributions of parameter values. (Contains 6 figures, 1 table and 1 footnote.)