Chapter 8 links diffusion models to linear system models of visual encoding, which leads to models with time-varying drift rates. These models apply to near-threshold detection (Yes/No accuracy) and simple reaction time tasks in which decisions are based on the outputs of transient and sustained mechanisms that respond either to stimulus onset and offset transients or to steady-state intensity levels, respectively. These mechanisms are represented by diffusion processes with drift rates that either increase to a maximum and then decrease to zero for transient mechanisms or increase to an asymptote for sustained mechanisms. The chapter evaluates the response time and accuracy predictions of these kinds of models, together with their associated hazard functions, in simple reaction time and temporal integration tasks and contrasts them to the predictions of a simple, constant-drift diffusion model in which a proportion of stimuli are not detected because the drift rate is negative or zero.