Overview
Flow matching models have become a cornerstone of modern generative modeling in 2026, powering applications from image synthesis to scientific simulation. Yet many downstream tasks require that generated samples satisfy prescribed constraints—observed measurements, physical laws, or safety specifications. Existing constrained samplers face a persistent trade-off: enforcing constraints often displaces samples far from the pretrained data distribution, degrading generative fidelity.
To address this, researchers Yesom Park, Kelvin Kan, Qifan Chen, Thomas Flynn, Hayden Schaeffer, and Xihaier Luo introduce MintFlow, a training-free constrained sampling framework that formulates constraint enforcement as a minimal intervention on the pretrained flow trajectory.
Core Idea
MintFlow seeks the smallest possible perturbation of an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. Key properties:
- Minimal perturbation, unchanged flow field. By perturbing only the flow state while keeping the pretrained flow field intact, MintFlow enforces the constraint while minimizing unnecessary deviation from the pretrained distribution.
- Closed-form solution. An adjoint formulation yields a closed-form expression for the required perturbation, eliminating the need for expensive iterative optimization.
- Adaptive intervention timing. MintFlow adaptively selects when to intervene, balancing the required perturbation magnitude against its amplification by the remaining flow.
Why It Matters in 2026
As flow matching has matured into a dominant generative paradigm, the demand for controllable, constraint-aware sampling has intensified—particularly in physics-informed and safety-critical applications. MintFlow's training-free nature makes it directly applicable to existing pretrained models without retraining or fine-tuning, a significant practical advantage as foundation-scale flow models become increasingly costly to adapt.
Results
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.
Paper Details
- Title: MintFlow: Minimal Trajectory Intervention for Constrained Flow Matching
- Authors: Yesom Park, Kelvin Kan, Qifan Chen, Thomas Flynn, Hayden Schaeffer, Xihaier Luo
- Subject: Artificial Intelligence (cs.AI)
- Submitted: 30 Sep 2026
- arXiv: arXiv:2610.02260
- DOI: 10.48550/arXiv.2610.02260
via ArXiv AI