HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization

Summary

HardFlow is a framework for hard-constrained sampling in flow-matching generative models, which reformulates constraint enforcement as a trajectory optimization problem solved with numerical optimal control and model predictive control techniques. The method steers sampling so constraints hold precisely at the terminal time, rather than projecting the entire path onto the constraint manifold as prior approaches do. Experiments in robotics planning, PDE boundary control and text-guided image editing report that HardFlow substantially outperforms existing methods on constraint satisfaction and sample quality.