Researchers propose MintFlow, a training-free framework to enforce constraints in flow matching models while preserving data distribution fidelity

Researchers from Carnegie Mellon University, the University of California, and collaborators introduce MintFlow, a training-free framework designed to enforce constraints on samples generated by flow matching models without substantially displacing them from the pretrained data distribution.

The core idea is to formulate constraint enforcement as a minimal intervention on the pretrained flow trajectory. MintFlow achieves this by identifying the smallest perturbation to an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. This approach minimizes unnecessary deviation from the pretrained distribution while keeping the pretrained flow field unchanged.

The framework leverages an adjoint formulation to derive a closed-form expression for the required perturbation, eliminating the need for expensive iterative optimization. Additionally, MintFlow adaptively selects the intervention time to balance the magnitude of the perturbation with its potential amplification by the remaining flow, further improving efficiency and effectiveness.

Across a range of tasks in generative vision and physical system modeling, MintFlow achieves competitive constraint satisfaction while preserving the pretrained generative distribution substantially better than state-of-the-art constrained methods. The authors attribute this performance to the minimal and targeted nature of the interventions, which avoid the distributional drift often observed in other constrained sampling approaches.