Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations observed in practical large-scale diffusion models. Offset noise has been proposed as an empirical solution to this issue, yet its theoretical basis remains insufficiently explored. In this paper, we propose a novel diffusion model that naturally incorporates additional noise within a rigorous probabilistic framework. Our approach modifies both the forward and reverse diffusion processes, enabling inputs to be diffused into Gaussian distributions with arbitrary mean structures. We derive a loss function based on the evidence lower bound and show that the resulting objective is structurally analogous to that of offset noise, with time-dependent coefficients. Experiments on controlled synthetic datasets demonstrate that the proposed model mitigates brightness-related limitations and achieves improved performance over conventional methods, particularly in high-dimensional settings.

翻译：扩散模型已成为机器学习中数据分布建模的基础工具。尽管这些模型取得了成功，但在生成具有极端亮度值的数据时仍面临挑战，这一点在实际大规模扩散模型观察到的局限性中得到了证实。偏移噪声已被提出作为解决该问题的经验性方法，但其理论基础仍未被充分探索。本文提出一种新颖的扩散模型，在严格的概率框架内自然地整合了额外噪声。我们的方法同时修正了前向和反向扩散过程，使输入能够扩散到具有任意均值结构的高斯分布中。我们基于证据下界推导了损失函数，并证明所得目标函数在结构上与偏移噪声的目标函数相似，且包含时间依赖系数。在受控合成数据集上的实验表明，所提模型减轻了亮度相关的局限性，并在高维设置下取得了优于传统方法的性能提升。