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 64 64 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.

In addition, minimizing log L(y, ŷ) is equivalent to minimizing L(y, ŷ). Similarly, to illustrate the effectiveness and robustness of our method in the non-incremental setting. We report our results after the first learning step on the ADE20K 100-50 (Table 3) and Cityscapes 11-5 (Table 4) benchmarks. Our proposed fairness approach has also contributed to the performance improvement of both major and minor classes in non-incremental settings. The comparison table of major and minor groups in the first step is illustrated below.

We introduce Meta-AdaM, a meta-learned adaptive optimizer with momentum, designed for few-shot learning tasks that pose significant challenges to deep learning models due to the limited number of labeled examples. Meta-learning has been successfully employed to address these challenges by transferring meta-learned prior knowledge to new tasks. Most existing works focus on meta-learning an optimal model initialization or an adaptive learning rate learner for rapid convergence. However, these approaches either neglect to consider weight-update history for the adaptive learning rate learner or fail to effectively integrate momentum for fast convergence, as seen in many-shot learning settings. To tackle these limitations, we propose a meta-learned learning rate learner that utilizes weight-update history as input to predict more appropriate learning rates for rapid convergence. Furthermore, for the first time, our approach incorporates momentum into the optimization process of few-shot learning via a double look-ahead mechanism, enabling rapid convergence similar to many-shot settings. Extensive experimental results on benchmark datasets demonstrate the effectiveness of the proposed Meta-AdaM.