Rectified Flow

Each successive reflow round is expected to produce a velocity field closer to linear, enabling few-step or single-step generation. On the Checkerboard benchmark, vanilla RectFlow achieves SWD near 0.166 at both k=1 and k=2, no better than the base Flow Matching model, confirming that the bottleneck is the coupling integrator. Rectified Flow addresses trajectory curvature by iteratively regenerating coupling data through forward integration of the previously trained model, then retraining on those self-generated pairs. Image generation experiments evaluate only k=1 reflow because training costs scale with the number of rounds, leaving multi-round rectification on images undemonstrated. In practice, the compounding improvement of iterative rectification fails because the bottleneck is the quality of the coupling integrator, not the loss function or model capacity.