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.

通过每个时间步骤在图像生成过程中优化纠缠的分布，以及通过降低维度但仍保持扰动参考图像高度集中的构建流形的块自适应实例归一化模块，新的基于分数分解扩散模型 (SDDM) 在多个 I2I 基准测试中表现优于现有的基于分数的扩散模型 (SBDM) 方法。

SDDM：用于非配对图像到图像转换的基于得分分解的流形扩散模型