用卷积替代加性噪声，让扩散模型更真实地处理图像模糊问题
Stop Denoising Your Blurs
- 用卷积构建从清晰图到模糊图的渐进轨迹，而非传统加噪
- 在高斯模糊上实现闭式解，中间状态物理可解释
- 框架可扩展至其他模糊类型，适合图像恢复研究者
近期扩散模型在图像修复任务中表现卓越，其核心依赖于退化前假设——退化过程以加性噪声为主。然而，模糊模型（如卷积模糊）违背此假设，因其本质为卷积操作而非加法。本文提出ConvDiff，一种基于扩散的新框架，将加性操作替换为卷积，用于图像去模糊。前向过程中，利用卷积在频域的特性，构建从清晰图像到模糊图像的有意义轨迹，而非逐步添加噪声。当前工作以高斯模糊为例，其频域分解可得闭式解且物理意义明确；该原理可自然推广至其他模糊类型。该方法弥合了模糊数学原理与扩散算法迭代设计间的鸿沟，使图像修复模型更具物理合理性与有效性。
原文摘要 · Abstract (English)
In recent times, diffusion models have achieved remarkable performance in image restoration tasks. Their core mechanism relies on the restricted presumption of degradation prior to the additive noise operation. However, the blur model, one of the most widely studied degradation formulations, violates this assumption, as it is inherently based on convolution rather than addition. In this paper, we introduce ConvDiff, a novel diffusion based framework that substitutes the additive operation with convolution for the task of image deblurring. In the forward process, we construct a meaningful trajectory from the clean image to its blurred counterpart by exploiting the frequency domain characteristics of convolution, rather than progressively corrupting the image with additive noise. While the current work instantiates this framework for Gaussian blur, where frequency-domain decomposition yields closed-form and physically valid intermediate states, the underlying principle of constructing degradation trajectories from the blur operator extends naturally to other blur families. This formulation bridges the gap between the mathematical principles of blurring and the iterative design of diffusion-based restoration algorithms, enabling more physically grounded and effective image restoration models.
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