Diffusion models have become fundamental tools for modeling data distributions in machine learning and have applications in image generation, drug discovery, and audio synthesis. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations in widely used frameworks like Stable Diffusion. 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 generalized 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, establishing its theoretical equivalence to offset noise with certain adjustments, while broadening its applicability. Experiments on synthetic datasets demonstrate that our model effectively addresses brightness-related challenges and outperforms conventional methods in high-dimensional scenarios.

翻译：扩散模型已成为机器学习中建模数据分布的基本工具，在图像生成、药物发现和音频合成等领域具有广泛应用。尽管取得了成功，这些模型在生成具有极端亮度值的数据时仍面临挑战，这一点在Stable Diffusion等广泛使用的框架中已得到证实。偏移噪声已被提出作为该问题的经验性解决方案，但其理论基础尚未得到充分探索。本文提出了一种广义扩散模型，能够在严格的概率框架内自然地引入额外噪声。我们的方法同时修改了前向和反向扩散过程，使得输入能够扩散至具有任意均值结构的高斯分布。基于证据下界，我们推导出一个损失函数，证明了其在特定调整下与偏移噪声的理论等价性，同时拓宽了其适用范围。在合成数据集上的实验表明，我们的模型能有效解决与亮度相关的挑战，并在高维场景中优于传统方法。