Training-free Linear Image Inversion via Flows

Training-free linear inversion involves the use of a pretrained generative model and -- through appropriate modifications to the generation process -- solving inverse problems without any finetuning of the generative model. While recent prior 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 image inversion 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 image inversion problems on high-dimensional datasets, ImageNet-64/128 and AFHQ-256, and we observe that our flow-based method for image inversion significantly improves upon closely-related diffusion-based linear inversion methods.