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.

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