Flow Along the K-Amplitude for Generative Modeling

weitao Du, Shuning Chang, Jiasheng Tang, Yu Rong, Fan Wang, Shengchao Liu

Track: long paper (up to 8 pages)

Keywords: K-Flow Matching, K-amplitude space, flow matching, generative modeling

Abstract: 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 of 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 and class-conditional image generation. Additionally, we conduct three ablation studies to demonstrate how K-Flow steers the scaling parameter to control the resolution of image generation.

Submission Number: 13