  Straightening the probability flow of the continuous-time generative models,
such as diffusion models or flow-based models, is the key to fast sampling
through the numerical solvers, existing methods learn a linear path by directly
generating the probability path the joint distribution between the noise and
data distribution. One key reason for the slow sampling speed of the ODE-based
solvers that simulate these generative models is the global truncation error of
the ODE solver, caused by the high curvature of the ODE trajectory, which
explodes the truncation error of the numerical solvers in the low-NFE regime.
To address this challenge, We propose a novel method called SeqRF, a learning
technique that straightens the probability flow to reduce the global truncation
error and hence enable acceleration of sampling and improve the synthesis
quality. In both theoretical and empirical studies, we first observe the
straightening property of our SeqRF. Through empirical evaluations via SeqRF
over flow-based generative models, We achieve surpassing results on CIFAR-10,
CelebA-$64 \times 64$, and LSUN-Church datasets.
