扩散模型像画家一样生成图像：先轮廓后细节的解析理论
Diffusion Models Generate Images Like Painters: an Analytical Theory of Outline First, Details Later
AI总结：
本文分析了扩散模型逆向生成过程，发现其具有低维轨迹、先轮廓后细节及早期扰动影响大的特性，通过推导高斯分布下概率流 ODE 的闭式解予以理论解释，并揭示了其与 GAN 生成及图像检索的联系。
摘要：
扩散生成模型如何将纯噪声转化为有意义的图像？在多种预训练扩散模型（包括如 Stable Diffusion 的条件潜在空间模型）中，我们观察到作为图像生成基础的逆向扩散过程具有以下性质：(i) 单条轨迹倾向于低维并类似于 2D “旋转”；(ii) 高方差场景特征（如布局）倾向于更早出现，而低方差细节倾向于更晚出现；(iii) 早期扰动对图像内容的影响通常大于后期扰动。为理解这些现象，我们推导并研究了高斯分布下概率流 ODE 的闭式解，表明逆向扩散状态向图像流形上逐渐明确的目标旋转。它还表明生成过程首先确定轮廓，然后才是越来越精细的细节。我们发现该解准确描述了预训练模型图像生成的初始阶段，且原则上可通过跳过逆向扩散步骤使图像生成更高效。最后，我们利用该解刻画了 Stable Diffusion 中的图像流形。我们的视角揭示了 GAN 与扩散生成之间意想不到的相似性，并在扩散与图像检索之间建立了概念联系。
英文摘要：
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.
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