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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19353 |
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| _version_ | 1866908340065402880 |
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| author | Du, Weitao Chang, Shuning Tang, Jiasheng Rong, Yu Wang, Fan Liu, Shengchao |
| author_facet | Du, Weitao Chang, Shuning Tang, Jiasheng Rong, Yu Wang, Fan Liu, Shengchao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flow Along the K-Amplitude for Generative Modeling Du, Weitao Chang, Shuning Tang, Jiasheng Rong, Yu Wang, Fan Liu, Shengchao Machine Learning Artificial Intelligence 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. |
| title | Flow Along the K-Amplitude for Generative Modeling |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2504.19353 |