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}

翻译：近年来，去噪扩散概率模型（DDPM）引起了广泛关注。通过构建一个从数据域开始、逐步添加噪声直至纯白噪声的马尔可夫过程，该类模型在学习数据分布方面表现出卓越性能。然而，这些模型需要大量扩散步骤才能生成美观样本，效率低下。此外，与常见生成对抗网络不同，扩散模型的潜空间不具备可解释性。本文提出将去噪扩散过程泛化为上采样扩散概率模型（UDPM），该模型在传统噪声水平添加基础上同时降低潜变量维度。因此，我们仅需7个扩散步骤即可采样出尺寸为256×256的图像，步数比标准DDPM减少两个数量级。我们正式建立了UDPM的马尔可夫扩散过程，并在流行的FFHQ、LSUN马匹、ImageNet和AFHQv2数据集上验证了其生成能力。UDPM的另一优势是易于对其潜空间进行插值，而标准扩散模型则不具备这一特性。我们的代码已在线上公开：\url{https://github.com/shadyabh/UDPM}