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

2025-11-08

AI Summary

Existing flow-based inverse problem solvers suffer from high computational cost due to pixel-space modeling and inaccurate posterior sampling caused by prior-agnostic covariance guidance. This work proposes LFlow—a training-free linear inverse solver that leverages a pre-trained autoencoder to map observations into a latent space, where efficient ODE-based sampling is performed via flow matching. Crucially, we derive the posterior covariance analytically from optimal vector field theory to enable precise, theoretically grounded flow guidance. Our key contributions are: (i) the first integration of flow matching into the latent space for fine-grained reconstruction, and (ii) a provably optimal covariance-guidance mechanism. Experiments demonstrate that LFlow outperforms state-of-the-art latent diffusion solvers across diverse inverse problems—achieving superior reconstruction fidelity, scalability to high-resolution images, and rapid inference—without requiring any task-specific training.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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 .

Problem

• Solving linear inverse problems using latent flow priors
• Overcoming computational limitations of pixel-space flow models
• Improving posterior alignment through theoretically grounded covariance guidance

Innovation

• Uses pretrained latent flow priors for inverse problems
• Performs ODE sampling in latent space efficiently
• Introduces theoretically grounded posterior covariance for guidance