Iso-Diffusion: Improving Diffusion Probabilistic Models Using the Isotropy of the Additive Gaussian Noise

Abstract: Denoising Diffusion Probabilistic Models (DDPMs) have accomplished much in the realm of generative AI. With the tremendous level of popularity the Generative AI algorithms have achieved, the demand for higher levels of performance continues to increase. Under this backdrop, careful scrutinization of algorithm performance under sample fidelity type measures is essential to ascertain how, effectively, the underlying structures of the data distribution were learned. In this context, minimizing the mean squared error between the additive and predicted noise alone does not impose structural integrity constraints on the predicted noise, for instance, isotropic. Under this premise, 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, and the results clearly indicate how the structural imposition was effective.