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arXiv · 2411.09356

Multi-scale Generative Modeling for Fast Sampling

Xiongye Xiao·Shixuan Li·Luzhe Huang·Gengshuo Liu·Trung-Kien Nguyen·Yi Huang·Di Chang·Mykel J. Kochenderfer·Paul Bogdan
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Abstract

While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a promising alternative. However, within the wavelet domain, we encounter unique challenges, especially the sparse representation of high-frequency coefficients, which deviates significantly from the Gaussian assumptions in the diffusion process. To this end, we propose a multi-scale generative modeling in the wavelet domain that employs distinct strategies for handling low and high-frequency bands. In the wavelet domain, we apply score-based generative modeling with well-conditioned scores for low-frequency bands, while utilizing a multi-scale generative adversarial learning for high-frequency bands. As supported by the theoretical analysis and experimental results, our model significantly improve performance and reduce the number of trainable parameters, sampling steps, and time.

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Xiongye Xiao, Shixuan Li, Luzhe Huang, Gengshuo Liu, Trung-Kien Nguyen, Yi Huang, Di Chang, Mykel J. Kochenderfer, Paul Bogdan. 2024-11-14. Multi-scale Generative Modeling for Fast Sampling. https://arxiv.org/abs/2411.09356

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