FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
On the diagonal s = t, the Lagrangian equation implies vt,t(x) =b t(x),(25) i.e., the parameterized velocity recovers the probability flow drift
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