Abstract
The success of diffusion models has driven interest in performing conditional sampling via training-free guidance of the denoising process to solve image restoration and other inverse problems. A popular class of methods, based on Diffusion Posterior Sampling (DPS), attempts to approximate the intractable posterior score function directly. In this work, we present a novel expression for the exact posterior score for purely denoising tasks that is tractable in terms of the unconditional score function. We leverage this result to analyze the time-dependent error in the DPS score for denoising tasks and compute step sizes on the fly to minimize the error at each time step. We demonstrate that these step sizes are transferable to related inverse problems such as colorization, random inpainting, and super resolution. Despite its simplicity, this approach is competitive with state-of-the-art techniques and enables sampling with fewer time steps than DPS.
Abstract (translated)
扩散模型的成功激发了人们通过无训练的去噪过程引导进行条件采样，以解决图像恢复和其他逆向问题的兴趣。基于扩散后验采样（DPS）的一类流行方法试图直接近似难以处理的后验评分函数。在这项工作中，我们提出了一个全新的、对于纯去噪任务而言可操作的确切后验评分表达式，并且该表达式可以用无条件评分函数来表示。利用这一结果，我们分析了DPS在去噪任务中的时间依赖误差，并实时计算步长以减少每个时间点的误差。我们展示了这些步长可以转移到相关逆向问题中，例如着色、随机插值和超分辨率。 尽管这种方法简单，但它与最先进的技术竞争性很强，并且可以在比DPS更少的时间步骤内进行采样。
URL
https://arxiv.org/abs/2506.13614
