Training-free Linear Image Inverses Via Flows

Solving inverse problems without any training involves using a pretrainedgenerative model and making appropriate modifications to the generation processto avoid finetuning of the generative model. While recent methods have exploredthe use of diffusion models, they still require the manual tuning of manyhyperparameters for different inverse problems. In this work, we propose atraining-free method for solving linear inverse problems by using pretrainedflow models, leveraging the simplicity and efficiency of Flow Matching models,using theoretically-justified weighting schemes, and thereby significantlyreducing the amount of manual tuning. In particular, we draw inspiration fromtwo main sources: adopting prior gradient correction methods to the flowregime, and a solver scheme based on conditional Optimal Transport paths. Aspretrained diffusion models are widely accessible, we also show how topractically adapt diffusion models for our method. Empirically, our approachrequires no problem-specific tuning across an extensive suite of noisy linearinverse problems on high-dimensional datasets, ImageNet-64/128 and AFHQ-256,and we observe that our flow-based method for solving inverse problems improvesupon closely-related diffusion-based methods in most settings.