Diffusion models (DMs) are a type of generative model that has a huge impact
on image synthesis and beyond. They achieve state-of-the-art generation results
in various generative tasks. A great diversity of conditioning inputs, such as
text or bounding boxes, are accessible to control the generation. In this work,
we propose a conditioning mechanism utilizing Gaussian mixture models (GMMs) as
feature conditioning to guide the denoising process. Based on set theory, we
provide a comprehensive theoretical analysis that shows that conditional latent
distribution based on features and classes is significantly different, so that
conditional latent distribution on features produces fewer defect generations
than conditioning on classes. Two diffusion models conditioned on the Gaussian
mixture model are trained separately for comparison. Experiments support our
findings. A novel gradient function called the negative Gaussian mixture
gradient (NGMG) is proposed and applied in diffusion model training with an
additional classifier. Training stability has improved. We also theoretically
prove that NGMG shares the same benefit as the Earth Mover distance
(Wasserstein) as a more sensible cost function when learning distributions
supported by low-dimensional manifolds.

利用高斯混合模型作为特征条件引导去噪过程，构建了一种基于高斯混合模型的条件机制，证明了该条件机制在特征上的条件潜在分布相较于类别上的条件潜在分布产生较少的缺陷生成，通过两种基于高斯混合模型的扩散模型的实验结果支持上述发现，并提出负高斯混合梯度作为一种新的梯度函数，通过额外分类器在扩散模型训练中应用，提高了训练稳定性，并从理论上证明了负高斯混合梯度和地球移动距离（Wasserstein 距离）在学习由低维流形支持的分布时具有相同的优势作为一种更合理的代价函数。