用混合高斯作先验，提升扩散模型对结构数据的建模能力。
Structured Diffusion Models with Mixture of Gaussians as Prior Distribution
- 以混合高斯替代标准高斯作为先验，融入数据结构信息。
- 理论证明新模型优于传统扩散模型，实验验证其鲁棒性。
- 适合资源有限或需实时训练的场景，实现快速稳定生成。
我们提出一类结构化扩散模型，将先验分布设为混合高斯而非标准高斯分布。通过选择特定混合高斯先验，可引入数据的结构信息。开发了一种简单可行的训练方法，可平滑地使用混合高斯作为先验。理论分析量化了所提模型相比经典扩散模型的优势。在合成数据、图像及实际运行数据上的数值实验表明，该模型具有明显优势。方法对先验设定错误具有鲁棒性，尤其适用于训练资源受限或需实时训练的场景。
原文摘要 · Abstract (English)
We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to incorporate certain structured information of the data. We develop a simple-to-implement training procedure that smoothly accommodates the use of mixed Gaussian as prior. Theory is provided to quantify the benefits of our proposed models, compared to the classical diffusion models. Numerical experiments with synthetic, image and operational data are conducted to show comparative advantages of our model. Our method is shown to be robust to mis-specifications and in particular suits situations where training resources are limited or faster training in real time is desired.
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