# Constant Acceleration Flow

**Authors:** Dogyun Park, Sojin Lee, Sihyeon Kim, Taehoon Lee, Youngjoon Hong, Hyunwoo J. Kim  
**arXiv:** [2411.00322](https://arxiv.org/abs/2411.00322)  
**Date:** 2024-11-01  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.00322v1/

## Key points

- Rectified flow and reflow procedures have advanced ODE flows by approximating image and noise pairs as linear trajectories with constant velocity.
- Constant velocity modeling and reflow processes may limit accurately capturing straight trajectories between pairs, affecting performance in few-step generation tasks.
- The introduction of Constant Acceleration Flow (CAF) addresses these limitations by incorporating acceleration as a learnable variable for more precise estimation of the ODE flow.
- CAF framework includes techniques such as initial velocity conditioning for the acceleration model and a reflow process for the initial velocity to enhance estimation accuracy.
- Extensive studies on various datasets have shown CAF's superior performance over state-of-the-art baselines, particularly in one-step generation tasks, preserving few-step couplings, and inversion compared to Rectified flow methods.
- Availability of code for CAF enhances its accessibility and applicability in research and practical applications.

## Summary

In the realm of fast generation techniques, rectified flow and reflow procedures have made significant strides in straightening ordinary differential equation (ODE) flows. These methods operate on the premise that image and noise pairs, referred to as couplings, can be approximated by linear trajectories with constant velocity. However, it has been noted that relying on constant velocity modeling and reflow processes may pose limitations in accurately capturing straight trajectories between pairs, leading to suboptimal performance in few-step generation tasks. To overcome these challenges, a groundbreaking framework known as Constant Acceleration Flow (CAF) has been introduced. CAF is built upon a simple constant acceleration equation that introduces acceleration as an additional learnable variable. This innovation allows for a more expressive and precise estimation of the ODE flow compared to traditional approaches. Furthermore, two key techniques have been proposed to enhance estimation accuracy within the CAF framework: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Extensive studies conducted on various datasets including toy datasets, CIFAR-10, and ImageNet 64x64 have demonstrated the superior performance of CAF over state-of-the-art baselines specifically in one-step generation tasks. Moreover, CAF has shown remarkable improvements in preserving few-step couplings and inversion compared to Rectified flow methods. The availability of code for CAF further enhances its accessibility and applicability in research and practical applications. Authored by Dogyun Park, Sojin Lee, Sihyeon Kim, Taehoon Lee, Youngjoon Hong, and Hyunwoo J. Kim,"Constant Acceleration Flow" presents a novel approach that pushes the boundaries of fast generation techniques by leveraging acceleration as a key variable in ODE flow estimation. This innovative framework holds promise for advancing generative modeling capabilities across various domains within machine learning and artificial intelligence research.