Constant Acceleration Flow
This work addresses a specific bottleneck in fast generation models for image synthesis, offering incremental improvements over existing methods.
The paper tackled the problem of suboptimal performance in few-step generation due to limitations in modeling straight trajectories with constant velocity in rectified flow and reflow procedures, and introduced Constant Acceleration Flow (CAF) with acceleration as a learnable variable, resulting in outperforming state-of-the-art baselines for one-step generation and improving coupling preservation and inversion.
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 \href{https://github.com/mlvlab/CAF}{https://github.com/mlvlab/CAF}.