Constant Acceleration Flow
Authors: name: Dogyun Park, name: Sojin Lee, name: Sihyeon Kim, name: Taehoon Lee, name: Youngjoon Hong, name: Hyunwoo J. Kim

Rectified flow and reflow procedures have significantly advanced fast
generation by progressively straightening ordinary differential equation (ODE)
flows. They operate under the assumption that image and noise pairs, known as
couplings, can be approximated by straight trajectories with constant velocity.
However, we observe that modeling with constant velocity and using reflow
procedures have limitations in accurately learning straight trajectories
between pairs, resulting in suboptimal performance in few-step generation. To
address these limitations, we introduce Constant Acceleration Flow (CAF), a
novel framework based on a simple constant acceleration equation. CAF
introduces acceleration as an additional learnable variable, allowing for more
expressive and accurate estimation of the ODE flow. Moreover, we propose two
techniques to further improve estimation accuracy: initial velocity
conditioning for the acceleration model and a reflow process for the initial
velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet
64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step
generation. We also show that CAF dramatically improves few-step coupling
preservation and inversion over Rectified flow. Code is available at
https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.