Constrained Flow Matching via Lagrangian Dual Flows
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 subproblem...
| Authors | Vince Kurtz, Alexander Davydov |
|---|---|
| Primary category | math.OC |
| Published | 5 July 2026 |
| Last updated at source | 30 September 2026 |
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