Constrained Flow Matching via Lagrangian Dual Flows

תקציר מקורי באנגליתarXiv:2607.04513v2 Announce Type: replace-cross 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