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ConicFlow: constrained Inference-time optimal control for flow matching models

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Briefings

ConicFlow proposes a new method for flow matching models that treats constrained sampling at inference time as an optimal control problem. The approach discretizes the problem and uses a receding-horizon primal-dual algorithm to optimize a short trajectory window at each step. It balances deviation from the pretrained flow against a reward, subject to hard terminal constraints. Experiments show ConicFlow achieves high reward and strong constraint satisfaction while deviating less from the pretrained flow than recent baselines.

Key points

• ConicFlow frames constrained sampling from flow matching models at inference time as an optimal control problem balancing deviation from the pretrained trajectory against reward.
• The method uses a receding-horizon primal-dual algorithm to optimize only a short window of the trajectory at each step for computational tractability.

Context

This work addresses the challenge of generating high-quality samples from flow matching models while maintaining adherence to specific constraints. The method offers a new approach to constrained inference-time control, potentially improving sample quality and constraint satisfaction in large-scale generative models.

Limitations

The study relies on standard regularity assumptions and convex-affine structure for theoretical guarantees. Results are limited to low- and high-dimensional settings with a recent large-scale flow matching model. Finite-horizon guarantees apply under these assumptions, and the terminal-estimate variant's tighter performance is shown only when flow dynamics change slowly.

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