What a Cheap Simulator Buys in Amortized Inference

Amortized simulation-based inference needs many simulations, so practitioners train on a cheaper approximate simulator and spend a limited budget of exact simulations where it seems most useful. Reported savings, not measured error, justify both choices. We measure the error, in stochastic gene-expression models whose exact posteriors are available. Three findings follow. First, mixing surrogate and exact simulations in one training objective shifts the estimator's target, with a posterior-mean bias that grows as $0.315(1-f{)}^{1.16}$ in the surrogate share $1-f$ ($r=0.97$). At every budget we measure, down to $160$ exact simulations, the mixture carries more bias and wider posteriors than training on the exact simulations alone and is never better calibrated, and a two-stage scheme that keeps the fidelities apart only ties the exact-only estimator. Second, placing the exact budget by burstiness is a weak lever. Even for a count surrogate whose error is concentrated, it improves on random placement by $0.003$ to $0.012$ in distance to nominal coverage, while reversing the same ordering costs $0.057$. Third, a classifier between the two simulators, with no neural posterior estimator and no reference posterior, reproduces the ordering of the trained estimators over six surrogate-system pairs and separates missing support from wrong shape. Matched controls trace the corruption to a continuum standing in for a discrete low-copy state, and the account carries over to a three-state promoter, a stochastic epidemic and public single-cell data. In our systems the approximation often costs more than the exact solver it replaces.