Abstract
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also generate samples from conditional distributions. In this paper, a novel diffusion-based framework is introduced for solving inverse problems using a piecewise guidance scheme. The guidance term is defined as a piecewise function of the diffusion timestep, facilitating the use of different approximations during high-noise and low-noise phases. This design is shown to effectively balance computational efficiency with the accuracy of the guidance term. Unlike task-specific approaches that require retraining for each problem, the proposed method is problem-agnostic and readily adaptable to a variety of inverse problems. Additionally, it explicitly incorporates measurement noise into the reconstruction process. The effectiveness of the proposed framework is demonstrated through extensive experiments on image restoration tasks, specifically image inpainting and super-resolution. Using a class conditional diffusion model for recovery, compared to the \pgdm baseline, the proposed framework achieves a reduction in inference time of \(25\%\) for inpainting with both random and center masks, and \(23\%\) and \(24\%\) for \(4\times\) and \(8\times\) super-resolution tasks, respectively, while incurring only negligible loss in PSNR and SSIM.
Abstract (translated)
扩散模型是一种强大的工具，能够通过逐步将纯噪声转化为结构化数据的去噪过程从高维分布中采样。当配备有引导机制时，这些模型也可以生成条件分布中的样本。在这篇论文中，提出了一种新的基于扩散框架的方法，用于采用分段引导方案解决逆向问题。该引导项被定义为扩散时间步长的分段函数，从而可以在高噪声和低噪声阶段使用不同的近似值。这种设计能够有效平衡计算效率与指导项的准确性之间的关系。不同于需要针对每个任务重新训练的任务特定方法，所提出的方法是无关任务的，并且可以轻松适应各种逆向问题。此外，它明确将测量噪声纳入到重建过程中。 通过广泛的图像恢复实验（具体为图像修复和超分辨率）展示了该框架的有效性。使用类条件扩散模型进行恢复时，与\pgdm基准方法相比，在随机掩码和中心掩码下的图像修补任务中，所提出的框架分别减少了25%的推理时间；在4倍和8倍超分辨率任务中，分别减少了23%和24%，同时仅造成了PSNR（峰值信噪比）和SSIM（结构相似性指数）上微不足道的质量损失。
URL
https://arxiv.org/abs/2507.18654
