Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Training-free Linear Image Inverses via Flows

Ashwini Pokle, Matthew J. Muckley, Ricky T. Q. Chen, Brian Karrer

TL;DR

This work tackles solving linear inverse problems without task-specific training by leveraging pretrained flow models and conditional Optimal Transport paths. It develops a training-free, flow-based inference framework that can utilize pretrained diffusion or flow models through a vector-field correction and a time-aware initialization, eliminating the need for problem-specific hyperparameter tuning. By demonstrating conversions between diffusion and flow representations and introducing the conditional OT flow sampling (OT-ODE), the authors show strong empirical performance on noisy degradations (deblurring, super-resolution, inpainting, denoising) across ImageNet variants and AFHQ, often surpassing diffusion-based baselines like PiGDM and RED-Diff. The approach is simple, robust, and scalable, offering a practical pathway to high-quality inverse problem solutions without additional training, with clear avenues for extending to non-linear, latent, or blind settings in future work.

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.

Training-free Linear Image Inverses via Flows

TL;DR

This work tackles solving linear inverse problems without task-specific training by leveraging pretrained flow models and conditional Optimal Transport paths. It develops a training-free, flow-based inference framework that can utilize pretrained diffusion or flow models through a vector-field correction and a time-aware initialization, eliminating the need for problem-specific hyperparameter tuning. By demonstrating conversions between diffusion and flow representations and introducing the conditional OT flow sampling (OT-ODE), the authors show strong empirical performance on noisy degradations (deblurring, super-resolution, inpainting, denoising) across ImageNet variants and AFHQ, often surpassing diffusion-based baselines like PiGDM and RED-Diff. The approach is simple, robust, and scalable, offering a practical pathway to high-quality inverse problem solutions without additional training, with clear avenues for extending to non-linear, latent, or blind settings in future work.

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.
Paper Structure (45 sections, 22 equations, 30 figures, 30 tables, 3 algorithms)

This paper contains 45 sections, 22 equations, 30 figures, 30 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation.
  4. Conditional diffusion models.
  5. Conditional flow models
  6. Gaussian probability paths.
  7. Training-free conditional inference using unconditional diffusion.
  8. Solving Linear Inverse Problems without Training via Flows
  9. Converting between diffusion models and flow models
  10. Correcting the vector field of flow models
  11. Starting flow sampling at time $t$ > 0.
  12. Algorithm summary.
  13. Experiments
  14. Datasets.
  15. Tasks.
  16. ...and 30 more sections

Figures (30)

  • Figure 1: Corrected images by solving linear inverse problems with flow models. For each pair of images, we show the noisy measurement (left) and the reconstruction (right).
  • Figure 2: Quantitative evaluation of pretrained VP-SDE model for solving linear inverse problems on super-resolution (SR), gaussian deblurring (GB), inpainting with centered (IPC) and freeform mask (IPF), and denoising (DN) with $\sigma_y=0.05$. We present results on face-blurred ImageNet-64 (INET-64), face-blurred ImageNet-128 (INET-128), and AFHQ.
  • Figure 3: Results for Gaussian deblurring with VP-SDE model and $\sigma_y=0.05$ for (first row) ImageNet-64, (second row) ImageNet-128, and (third row) AFHQ.
  • Figure 4: Results for super-resolution with VP-SDE model and $\sigma_y=0.05$ for (first row) ImageNet-64 $2\times$, (second row) ImageNet-128 $2\times$, and (third row) AFHQ $4\times$.
  • Figure 5: Results for inpainting (centered mask) with VP-SDE model and $\sigma_y=0.05$ for (first row) ImageNet-64, (second row) ImageNet-128, and (third row) AFHQ.
  • ...and 25 more figures