  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.
