Constant Acceleration Flow

TL;DR

Constant Acceleration Flow (CAF) introduces acceleration as a learnable variable in flow models, significantly enhancing the accuracy of trajectory learning and improving one-step and few-step image generation performance.

Contribution

CAF proposes a novel constant acceleration framework with techniques like initial velocity conditioning, outperforming existing methods in flow-based generative modeling.

Findings

Outperforms state-of-the-art baselines in one-step generation.

Dramatically improves few-step coupling preservation.

Effective on datasets like CIFAR-10 and ImageNet 64x64.

Abstract

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}.