Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving

TL;DR

LFlow introduces a training-free, latent space flow-based method for linear inverse problems, improving efficiency and reconstruction quality by leveraging optimal vector fields for guidance.

Contribution

It proposes a novel latent flow framework that operates without training, using flow matching and optimal vector fields for improved inverse problem solving.

Findings

Outperforms state-of-the-art latent diffusion methods in reconstruction quality

Operates efficiently in latent space, reducing computational costs for high-resolution images

Provides a theoretically grounded posterior covariance for better flow guidance

Abstract

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 .