通过拉格朗日对偶流进行约束流匹配
Constrained Flow Matching via Lagrangian Dual Flows
- DePaul University（德保罗大学）
- Rice University（里士满大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究在生成建模中加入推理时约束的问题，提出基于拉格朗日对偶动力学的拉格朗日对偶流技术，能保证非线性约束满足，算法简单有效并建立新理论联系。
AI中文摘要：
流匹配是生成建模的有力工具，但机器人、规划和物理中的新应用需要对生成输出进行推理时约束。此类约束通常复杂且高度非线性。本文介绍拉格朗日对偶流，一种基于拉格朗日对偶动力学的新的约束生成技术家族。
英文摘要：
Flow matching is a powerful tool for generative modeling, but emerging applications in robotics, planning, and control require inference-time constraints on generated outputs. Such constraints are often complex and highly nonlinear. As a result, methods designed for linear constraints like image inpainting are rarely sufficient, and projection or optimization-based alternatives can be prohibitively expensive. In this paper, we introduce Lagrangian Dual Flows, a new family of constrained generation techniques based on Lagrangian dual dynamics. By flowing a dual co-state alongside generated samples, we can guarantee nonlinear constraint satisfaction without expensive optimization subproblems, pseudoinverses, or projection steps during the denoising process. The resulting constrained generation algorithms are simple, effective, and open new theoretical connections between flow matching and primal-dual methods in numerical optimization.
