  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.
