Denoising Diffusion Probabilistic Models (DDPMs) have accomplished much in the realm of generative AI. Despite their high performance, there is room for improvement, especially in terms of sample fidelity by utilizing statistical properties that impose structural integrity, such as isotropy. Minimizing the mean squared error between the additive and predicted noise alone does not impose constraints on the predicted noise to be isotropic. Thus, we were motivated to utilize the isotropy of the additive noise as a constraint on the objective function to enhance the fidelity of DDPMs. Our approach is simple and can be applied to any DDPM variant. We validate our approach by presenting experiments conducted on four synthetic 2D datasets as well as on unconditional image generation. As demonstrated by the results, the incorporation of this constraint improves the fidelity metrics, Precision and Density for the 2D datasets as well as for the unconditional image generation.

翻译：去噪扩散概率模型（DDPMs）在生成式人工智能领域取得了显著成就。尽管其性能卓越，但仍有改进空间，尤其是在利用各向同性等统计特性施加结构完整性以提高样本保真度方面。仅最小化加性噪声与预测噪声之间的均方误差，并不能约束预测噪声具有各向同性。因此，我们受到启发，利用加性噪声的各向同性作为目标函数的约束条件，以提升DDPMs的保真度。我们的方法简单且可应用于任何DDPM变体。通过在四个合成二维数据集上以及无条件图像生成上进行的实验，我们验证了该方法。结果表明，引入该约束改善了二维数据集和无条件图像生成的保真度指标——精确度（Precision）和密度（Density）。