As a result, the reverse process gradually denoises and upsamples the latent variable to produce a sample from the data distribution.

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.

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 recent years, Denoising Diffusion Probabilistic Models (DDPM) have caught significant attention. By composing a Markovian process that starts in the data domain and then gradually adds noise until reaching pure white noise, they achieve superior performance in learning data distributions. Yet, these models require a large number of diffusion steps to produce aesthetically pleasing samples, which is inefficient. In addition, unlike common generative adversarial networks, the latent space of diffusion models is not interpretable. In this work, we propose to generalize the denoising diffusion process into an Upsampling Diffusion Probabilistic Model (UDPM), in which we reduce the latent variable dimension in addition to the traditional noise level addition. As a result, we are able to sample images of size $256\times 256$ with only 7 diffusion steps, which is less than two orders of magnitude compared to standard DDPMs. We formally develop the Markovian diffusion processes of the UDPM, and demonstrate its generation capabilities on the popular FFHQ, LSUN horses, ImageNet, and AFHQv2 datasets. Another favorable property of UDPM is that it is very easy to interpolate its latent space, which is not the case with standard diffusion models. Our code is available online \url{https://github.com/shadyabh/UDPM}