Many stochastic dynamical systems rely on either expensive experimental observation or simulations. However, often long-time-scale statistics are needed for actionable insights, e.g. invariant measures and time-correlations. Deep generative surrogate models such as implicit transfer operators (NeurIPS 2023, pioneered by PI) allow us to generate such statistics with 5 orders of magnitude speedup. However, we cannot guarantee the predictions are aligned with the underlying stochastic dynamics exactly. To overcome problem, we propose using neural density ratio estimation, to predict the probability of a path being generated from a biased model or from the ground truth model. Using this prediction we can use Girsanovs theorem to compute importance weights for path reweighing of efficient, yet biased dynamics, to unbiased dynamics, through our novel Marginalized Girsanov Reweighting approach. This project will close an important gap between efficient, yet biased surrogate models and unbiased numerical simulation based methods, closer aligning the two, enabling quantitative use of surrogates in scientific and engineering applications.