Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of correlated noise in computer graphics, its potential for improving the training process has been underexplored. In this paper, we introduce a novel and general class of diffusion models taking correlated noise within and across images into account. More specifically, we propose a time-varying noise model to incorporate correlated noise into the training process, as well as a method for fast generation of correlated noise mask. Our model is built upon deterministic diffusion models and utilizes blue noise to help improve the generation quality compared to using Gaussian white (random) noise only. Further, our framework allows introducing correlation across images within a single mini-batch to improve gradient flow. We perform both qualitative and quantitative evaluations on a variety of datasets using our method, achieving improvements on different tasks over existing deterministic diffusion models in terms of FID metric.

翻译：现有的大多数扩散模型在所有时间步长上使用高斯噪声进行训练和采样，这未必能最优地考虑去噪网络重建的频率内容。尽管相关噪声在计算机图形学中有多种应用，但其在改进训练过程方面的潜力尚未被充分探索。本文提出了一类新颖且通用的扩散模型，该模型考虑了图像内部及图像之间的相关噪声。具体而言，我们提出了一种时变噪声模型，以将相关噪声融入训练过程，并开发了一种快速生成相关噪声掩码的方法。我们的模型基于确定性扩散模型，并利用蓝噪声来提升生成质量，相较于仅使用高斯白（随机）噪声的方法有所改进。此外，我们的框架允许在单个小批量数据中引入图像之间的相关性，以改善梯度流。我们采用所提方法在多个数据集上进行了定性与定量评估，在FID指标上，相较于现有确定性扩散模型，我们在不同任务中均取得了改进。