Our point of departure is the standard simple drift diffusion model (DDM) due to its analytical tractability and its prevalence as the most common sequential sampling model (SSM) in cognitive neuroscience. By systematically varying different facets of the DDM, we test our likelihood approximation networks (LANs) across a range of SSMs for parameter recovery, goodness of fit (posterior predictive checks), and inference runtime. We divide the resulting models into four classes as indicated by the legend. We consider the simple DDM in the analytical likelihood (solid line) category, although, strictly speaking, the likelihood involves an infinite sum and thus demands an approximation algorithm introduced by Navarro and Fuss, but this algorithm is sufficiently fast to evaluate so that it is not a computational bottleneck. The full-DDM needs numerical quadrature (dashed line) to integrate over variability parameters, which inflates the evaluation time by 1–2 orders of magnitude compared to the simple DDM. Similarly, likelihood approximations have been derived for a range of models using the Fokker–Planck equations (dotted-dashed line), which again incurs nonsignificant evaluation cost. Finally, for some models no approximations exist and we need to resort to computationally expensive simulations for likelihood estimates (dotted line). Amortizing computations with LANs can substantially speed up inference for all but the analytical likelihood category (but see runtime for how it can even provide speedup in that case for large datasets).