Researchers introduce ConicFlow for constrained flow matching model sampling
It reframes constrained sampling from flow matching models as an optimal control problem at inference time. The approach balances deviations from the pretrained trajectory against a reward function while enforcing hard terminal constraints.
Key points
- ConicFlow reframes constrained sampling as an optimal control problem with hard terminal constraints
- Uses receding-horizon control and primal-dual algorithms for computational efficiency and feasibility
- Terminal-estimate variant reduces truncation errors and improves theoretical guarantees in experiments
ConicFlow uses receding-horizon control, optimizing only short trajectory windows for efficiency. A primal-dual algorithm refines dual multipliers to guide generation toward feasible final samples. A terminal-estimate variant reduces local truncation errors by evaluating rewards and constraints at the predicted endpoint. Under standard assumptions, the method guarantees finite-horizon suboptimality, with sharper bounds for convex-affine structures. Experiments in low- and high-dimensional settings show it outperforms recent baselines in reward, constraint satisfaction, and adherence to pretrained flows.
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