Inferring processes or constructs from performance data is a major hallmark of cognitive psychometrics. Particularly, diffusion modeling of response times (RTs) from correct and erroneous responses using the Wiener distribution has become a popular measurement tool because it provides a set of psychologically interpretable parameters. However, an important precondition to identify all of these parameters is a sufficient number of RTs from erroneous responses. In the present article, we show by simulation that the parameters of the Wiener distribution can be recovered from tasks yielding very high or even perfect response accuracies using the shifted Wald distribution. Specifically, we argue that error RTs can be modeled as correct RTs that have undergone censoring by using techniques from parametric survival analysis. We illustrate our reasoning by fitting the Wiener and (censored) shifted Wald distribution to RTs from six participants who completed a Go/No-go task. In accordance with our simulations, diffusion modeling using the Wiener and the shifted Wald distribution yielded identical parameter estimates when the number of erroneous responses was predicted to be low. Moreover, the modeling of error RTs as censored correct RTs substantially improved the recovery of these diffusion parameters when premature trial timeout was introduced to increase the number of omission errors. Thus, the censored shifted Wald distribution provides a suitable means for diffusion modeling in situations when the Wiener distribution cannot be fitted without parametric constraints.