用状态依赖扩散过程实现高效图像修复，一步到位不需来回迭代。
Efficient Image Restoration with State-Dependent Forward Diffusion
- 设计状态依赖的随机微分方程，让低质图像逐步向清晰图像收敛。
- 仅需几步采样即可达到与复杂模型相当的修复效果。
- 适合追求快速推理的图像修复应用，如实时处理或移动端部署。
本文提出一种基于状态依赖均值回归前向扩散（FoD）的图像修复方法。不同于传统扩散模型依赖前后向耦合过程，FoD仅通过单一前向扩散过程直接学习修复任务，构建出简洁高效的框架。其核心是包含漂移与扩散项中均值回归机制的状态依赖随机微分方程，驱动低质量数据以受控随机波动向干净图像端点演化，模拟源分布与目标分布间的随机插值。更重要的是，该模型解析可解，训练采用简单随机流匹配目标，支持推理阶段少步采样。尽管结构简单，该模型在多种图像修复任务上表现优于代表性扩散模型、扩散桥及流匹配方法。代码已开源：https://github.com/Algolzw/FoD。
原文摘要 · Abstract (English)
This paper proposes to perform image restoration through a state-dependent mean-reverting forward diffusion (FoD) process. In contrast to traditional diffusion-based approaches that rely on a coupled forward-backward diffusion scheme, FoD directly learns image restoration through a single forward diffusion process, yielding a simple yet efficient framework. The core of FoD is a state-dependent stochastic differential equation (SDE) that involves a mean-reverting term in both the drift and diffusion functions. This mean-reverting structure drives the low-quality data toward the clean endpoint with controlled stochastic variation, therefore simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling few-step sampling during inference. The proposed FoD model, despite its simplicity, achieves strong overall performance on various image restoration tasks compared to representative diffusion, diffusion bridge, and flow matching approaches. The code is available at https://github.com/Algolzw/FoD.
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