  Recently, diffusion model have demonstrated impressive image generation
performances, and have been extensively studied in various computer vision
tasks. Unfortunately, training and evaluating diffusion models consume a lot of
time and computational resources. To address this problem, here we present a
novel pyramidal diffusion model that can generate high resolution images
starting from much coarser resolution images using a {\em single} score
function trained with a positional embedding. This enables a neural network to
be much lighter and also enables time-efficient image generation without
compromising its performances. Furthermore, we show that the proposed approach
can be also efficiently used for multi-scale super-resolution problem using a
single score function.
