Training-free Linear Image Inverses via Flows

TL;DR

This paper introduces a training-free, flow-based method for solving linear inverse problems that reduces manual tuning and improves performance over diffusion-based approaches, using pretrained flow models and theoretically-justified weighting schemes.

Contribution

The authors propose a novel training-free approach leveraging pretrained flow models and optimal transport theory to solve linear inverse problems with minimal manual tuning.

Findings

Requires no problem-specific tuning across diverse datasets.

Outperforms diffusion-based methods in most tested scenarios.

Effective on high-dimensional datasets like ImageNet and AFHQ.

Abstract

Solving inverse problems without any training involves using a pretrained generative model and making appropriate modifications to the generation process to avoid finetuning of the generative model. While recent methods have explored the use of diffusion models, they still require the manual tuning of many hyperparameters for different inverse problems. In this work, we propose a training-free method for solving linear inverse problems by using pretrained flow models, leveraging the simplicity and efficiency of Flow Matching models, using theoretically-justified weighting schemes, and thereby significantly reducing the amount of manual tuning. In particular, we draw inspiration from two main sources: adopting prior gradient correction methods to the flow regime, and a solver scheme based on conditional Optimal Transport paths. As pretrained diffusion models are widely accessible, we also show how to practically adapt diffusion models for our method. Empirically, our approach requires no problem-specific tuning across an extensive suite of noisy linear inverse problems on high-dimensional datasets, ImageNet-64/128 and AFHQ-256, and we observe that our flow-based method for solving inverse problems improves upon closely-related diffusion-based methods in most settings.