Recent score-based diffusion models (SBDMs) show promising results in unpaired image-to-image translation (I2I). However, existing methods, either energy-based or statistically-based, provide no explicit form of the interfered intermediate generative distributions. This work presents a new score-decomposed diffusion model (SDDM) on manifolds to explicitly optimize the tangled distributions during image generation. SDDM derives manifolds to make the distributions of adjacent time steps separable and decompose the score function or energy guidance into an image ``denoising" part and a content ``refinement" part. To refine the image in the same noise level, we equalize the refinement parts of the score function and energy guidance, which permits multi-objective optimization on the manifold. We also leverage the block adaptive instance normalization module to construct manifolds with lower dimensions but still concentrated with the perturbed reference image. SDDM outperforms existing SBDM-based methods with much fewer diffusion steps on several I2I benchmarks.

翻译：最近的基于分数的扩散模型在无配对图像到图像翻译中展现出令人瞩目的成果。然而，现有方法（无论是基于能量还是基于统计的）均未给出受干扰中间生成分布的显式形式。本文提出了一种流形上的新型分数分解扩散模型，用于在图像生成过程中显式优化纠缠分布。SDDM推导出流形以使相邻时间步的分布可分离，并将分数函数或能量引导分解为图像"去噪"部分和内容"细化"部分。为在相同噪声水平下细化图像，我们均衡了分数函数与能量引导中的细化部分，从而允许在流形上进行多目标优化。我们还利用块自适应实例归一化模块构建维度更低但仍集中含有扰动参考图像的流形。在多个图像到图像翻译基准测试中，SDDM以更少的扩散步数优于现有基于分数的扩散模型方法。