DS-RectFlow

Once the coupling dataset is generated offline, DS-RectFlow inference uses plain Euler at zero added latency relative to vanilla RectFlow. On CIFAR-10 with Euler-20, DS-RectFlow at NFE=1 (FID 12.03) outperforms vanilla RectFlow at every tested NFE including NFE=20 (FID 14.38). Each corrected Euler step costs 81 model passes with m=n_h=8, applied only during offline coupling generation for the first fraction of integration steps. CIFAR-10 FID numbers are above state-of-the-art because the base model uses only 50,000 training iterations versus 400,000 used by Liu et al. (2023); the comparison is framed as isolating the correction's effect, not achieving peak absolute performance. DS-RectFlow suppresses divergence during offline coupling generation without changing the training loss, model architecture, or inference procedure. The correction displaces each integration particle to a nearby candidate state with smaller estimated divergence before each Euler step, leaving the velocity field itself unmodified. For image generation, the zeroth-order correction evaluates eight Gaussian-perturbed candidate states per step and selects the one with minimum estimated divergence. The authors pr…