发表机构
University of California, Los Angeles; Brookhaven National Laboratory（加州大学洛杉矶分校; 布鲁克海文国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
MintFlow提出免训练的约束流匹配框架，通过最小干预预训练流轨迹并采用闭式伴随解，在满足约束的同时显著保持生成分布，优于现有方法。
AI 中文摘要
流匹配模型在生成建模方面表现出色，许多下游应用要求其样本满足既定约束，如观测数据和物理定律。然而，现有的约束采样器常常面临权衡：强制执行约束会大幅使样本偏离预训练数据分布。为解决这一权衡问题，我们引入了MintFlow，一种免训练的约束采样框架，将约束执行表述为对预训练流轨迹的最小干预。MintFlow寻求对中间流状态的最小扰动，使其在预训练流场下的后续演化满足目标约束。通过最小程度地扰动流状态同时保持预训练流场不变，MintFlow在强制执行约束的同时，最小化了对预训练分布的不必要偏离。伴随公式为该扰动提供了闭式表达式，消除了昂贵的迭代优化。此外，MintFlow自适应地选择干预时间，以平衡所需扰动幅度与其被剩余流放大的效应。在生成视觉和物理系统建模的一系列任务中，MintFlow在实现具有竞争力的约束满足度的同时，比最先进的约束方法更好地保持了预训练生成分布。
英文摘要
Flow 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 perturbation, eliminating expensive iterative optimization. Furthermore, MintFlow adaptively selects the intervention time to balance the required perturbation magnitude with its amplification by the remaining flow. Across a range of tasks in generative vision and physical system modeling, MintFlow achieves competitive constraint satisfaction while preserving the pretrained generative distribution substantially better than state-of-the-art constrained methods.
