Plug-and-Play (PnP) methods with generative priors have achieved strong performance in inverse problems, with recent flow matching models enabling fast and scalable reconstruction. However, a key challenge in PnP methods is maintaining consistency between data fidelity updates and the learned generative prior, as data-consistency steps can move iterates away from the flow trajectory. We propose an ADMM-based PnP framework for flow matching priors that enforces stronger consistency between the measurement model and the prior through auxiliary variables and dual updates. In addition, we introduce a trajectory correction mechanism that restores consistency with the flow via a combination of deterministic and stochastic projections. Our method provides a more principled integration of flow priors within PnP frameworks, achieving high-quality reconstructions with reduced computational cost.

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