  Denoising Diffusion Probabilistic Models (DDPM) have recently gained
significant attention. DDPMs compose a Markovian process that begins in the
data domain and gradually adds noise until reaching pure white noise. DDPMs
generate high-quality samples from complex data distributions by defining an
inverse process and training a deep neural network to learn this mapping.
However, these models are inefficient because they require many diffusion steps
to produce aesthetically pleasing samples. Additionally, unlike generative
adversarial networks (GANs), the latent space of diffusion models is less
interpretable. In this work, we propose to generalize the denoising diffusion
process into an Upsampling Diffusion Probabilistic Model (UDPM). In the forward
process, we reduce the latent variable dimension through downsampling, followed
by the traditional noise perturbation. As a result, the reverse process
gradually denoises and upsamples the latent variable to produce a sample from
the data distribution. We formalize the Markovian diffusion processes of UDPM
and demonstrate its generation capabilities on the popular FFHQ, AFHQv2, and
CIFAR10 datasets. UDPM generates images with as few as three network
evaluations, whose overall computational cost is less than a single DDPM or EDM
step, while achieving an FID score of 6.86. This surpasses current
state-of-the-art efficient diffusion models that use a single denoising step
for sampling. Additionally, UDPM offers an interpretable and interpolable
latent space, which gives it an advantage over traditional DDPMs. Our code is
available online: \url{https://github.com/shadyabh/UDPM/}
