In this work, we propose a novel generative learning paradigm, K-Flow, an algorithm that flows along the $K$-amplitude. Here, $k$ is a scaling parameter that organizes frequency bands (or projected coefficients), and amplitude describes the norm of such projected coefficients. By incorporating the $K$-amplitude decomposition, K-Flow enables flow matching across the scaling parameter as time. We discuss three venues and six properties of K-Flow, from theoretical foundations, energy and temporal dynamics, and practical applications, respectively. Specifically, from the practical usage perspective, K-Flow allows steerable generation by controlling the information at different scales. To demonstrate the effectiveness of K-Flow, we conduct experiments on unconditional image generation, class-conditional image generation, and molecule assembly generation. Additionally, we conduct three ablation studies to demonstrate how K-Flow steers scaling parameter to effectively control the resolution of image generation.

本研究提出了一种新颖的生成学习范式K-Flow，该算法沿着K幅度流动。K-Flow通过纳入K幅度分解，提供了动态生成控制的能力，使得可以在不同尺度上调节信息。通过在无条件图像生成、类别条件图像生成和分子组装生成等方面的实验，验证了K-Flow在有效控制生成图像分辨率方面的显著效果。

沿K幅度流动的生成建模