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：大多数现有的扩散模型在所有时间步中使用高斯噪声进行训练和采样，这可能无法最优地反映去噪网络重构的频率内容。尽管相关噪声在计算机图形学中有广泛应用，但其在优化训练过程中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，将图像内部及图像之间的相关噪声纳入考量。具体而言，我们提出了一种时变噪声模型，将相关噪声融入训练过程，并给出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，利用蓝噪声相较于仅使用高斯白（随机）噪声可提升生成质量。此外，本框架允许在单个小批量内引入图像间的相关性以改善梯度流。我们在多个数据集上对该方法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，该方法在不同任务中均取得了性能提升。