Because many of our X-ray telescopes are optimized towards observing faint sources, observations of bright sources like X-ray binaries in outburst are often affected by instrumental biases. These effects include dead time and photon pile-up, which can dramatically change the statistical inference of physical parameters from these observations. While dead time is difficult to take into account in a statistically consistent manner, simulating dead time-affected data is often straightforward. This structure makes the issue of inferring physical properties from dead time-affected observations fall into a class of problems common across many scientific disciplines. There is a growing number of methods to address them under the name of Simulation-Based Inference (SBI), aided by new developments in density estimation and statistical machine learning. In this paper, we introduce SBI as a principled way to infer variability properties from dead time-affected light curves. We use Sequential Neural Posterior Estimation to estimate the posterior probability for variability properties. We show that this method can recover variability parameters on simulated data even when dead time is variable, and present results of an application of this approach to NuSTAR observations of the galactic black hole X-ray binary GRS 1915+105.