Recently, Rissanen et al., (2022) have presented a new type of diffusion
process for generative modeling based on heat dissipation, or blurring, as an
alternative to isotropic Gaussian diffusion. Here, we show that blurring can
equivalently be defined through a Gaussian diffusion process with non-isotropic
noise. In making this connection, we bridge the gap between inverse heat
dissipation and denoising diffusion, and we shed light on the inductive bias
that results from this modeling choice. Finally, we propose a generalized class
of diffusion models that offers the best of both standard Gaussian denoising
diffusion and inverse heat dissipation, which we call Blurring Diffusion
Models