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arXiv · 2504.19353

Flow Along the K-Amplitude for Generative Modeling

Weitao Du·Shuning Chang·Jiasheng Tang·Yu Rong·Fan Wang·Shengchao Liu
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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 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.

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Weitao Du, Shuning Chang, Jiasheng Tang, Yu Rong, Fan Wang, Shengchao Liu. 2025-04-27. Flow Along the K-Amplitude for Generative Modeling. https://arxiv.org/abs/2504.19353

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