arXiv：cs.LG· Vince Kurtz, Alexander Davydov·· 2 天前AI 评分35
Lagrangian Dual Flows：用拉格朗日对偶流实现非线性约束生成
Constrained Flow Matching via Lagrangian Dual Flows
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研究者提出 Lagrangian Dual Flows，一种基于拉格朗日对偶动力学的约束生成方法，通过让对偶协态随生成样本同步流动，在去噪过程中无需昂贵优化子问题、伪逆或投影步骤即可保证非线性约束满足。该方法面向机器人、规划与控制等需要在推理时施加复杂非线性约束的场景，并为 flow matching 与数值优化中的原始-对偶方法建立了新的理论联系。
正文
Abstract: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.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.04513 [math.OC] |
| (or arXiv:2607.04513v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2607.04513 arXiv-issued DOI via DataCite |
Submission history
From: Alexander Davydov [view email]
[v1]
Sun, 5 Jul 2026 21:25:51 UTC (1,019 KB)
[v2]
Wed, 30 Sep 2026 23:15:00 UTC (4,037 KB)
来源：arXiv：cs.LG · arxiv.org