Constrained Flow Matching via Lagrangian Dual Flows
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.
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BibTeX
@misc{kurtz2026constrained,
title = {{Constrained Flow Matching via Lagrangian Dual Flows}},
author = {Vince Kurtz and Alexander Davydov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04513},
eprint = {2607.04513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04513},
}
RIS
TY - UNPB
TI - Constrained Flow Matching via Lagrangian Dual Flows
AU - Vince Kurtz
AU - Alexander Davydov
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.04513
UR - https://arxiv.org/abs/2607.04513
AB - 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.
ER -