  While diffusion models have shown great success in image generation, their
noise-inverting generative process does not explicitly consider the structure
of images, such as their inherent multi-scale nature. Inspired by diffusion
models and the empirical success of coarse-to-fine modelling, we propose a new
diffusion-like model that generates images through stochastically reversing the
heat equation, a PDE that locally erases fine-scale information when run over
the 2D plane of the image. We interpret the solution of the forward heat
equation with constant additive noise as a variational approximation in the
diffusion latent variable model. Our new model shows emergent qualitative
properties not seen in standard diffusion models, such as disentanglement of
overall colour and shape in images. Spectral analysis on natural images
highlights connections to diffusion models and reveals an implicit
coarse-to-fine inductive bias in them.
