用流模型在潜在空间做无训练逆问题求解，提升图像重建质量。
Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
- 在潜在空间用流匹配进行无训练采样，路径更优效率更高。
- 引入理论推导的后验协方差，提升重建与生成轨迹对齐度。
- 无需训练，适用于高分辨率图像，适合快速部署的逆问题场景。
近期逆问题求解研究越来越多采用流先验替代扩散模型，因其能构建从噪声到数据的直线概率路径，显著提升训练与推理效率。然而现有基于流的逆求解器存在两大局限：(i) 直接在像素空间操作，训练耗时且难以扩展至高分辨率图像；(ii) 采用与先验无关的后验协方差引导策略，削弱与生成轨迹的对齐并降低后验覆盖能力。本文提出 LFlow（Latent Refinement via Flows），一种基于预训练潜在流先验的无训练线性逆问题求解框架。LFlow 利用流匹配在潜在空间中沿最优路径执行常微分方程采样，进一步通过最优向量场推导出理论上合理的后验协方差，实现有效流引导。实验表明，该方法在多数任务中优于当前最先进的潜在扩散求解器，在重建质量上表现更优。代码将公开于 https://github.com/hosseinaskari-cs/LFlow。
原文摘要 · Abstract (English)
Recent advances in inverse problem solving have increasingly adopted flow priors over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and inference. However, current flow-based inverse solvers face two primary limitations: (i) they operate directly in pixel space, which demands heavy computational resources for training and restricts scalability to high-resolution images, and (ii) they employ guidance strategies with prior-agnostic posterior covariances, which can weaken alignment with the generative trajectory and degrade posterior coverage. In this paper, we propose LFlow (Latent Refinement via Flows), a training-free framework for solving linear inverse problems via pretrained latent flow priors. LFlow leverages the efficiency of flow matching to perform ODE sampling in latent space along an optimal path. This latent formulation further allows us to introduce a theoretically grounded posterior covariance, derived from the optimal vector field, enabling effective flow guidance. Experimental results demonstrate that our proposed method outperforms state-of-the-art latent diffusion solvers in reconstruction quality across most tasks. The code will be publicly available at https://github.com/hosseinaskari-cs/LFlow .
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