Accurate signal predictions are essential for interpreting and optimizing fixed-target searches for new physics. Even in minimal models such as the dark photon () or millicharged particles (mCPs), theoretical uncertainties in hadronic production can be substantial. We introduce a data-driven framework that predicts both the rate and kinematic distributions of and mCP production directly from measured dilepton events, without relying on specific theoretical production models. This method uses the close correspondence between amplitudes for emission of or mCPs, and for off-shell Standard Model photon production, the latter being experimentally measurable in full differential form. We demonstrate that normalizing flow models can learn these distributions from data and serve as a fast, realistic Monte Carlo generator for dark sector signal simulations.

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