DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems
Shadab Ahamed, Eldad Haber
eess.IV, cs.AI, cs.CV, cs.LG
Submitted: 2026-02-28
Updated: 2026-08-19
Comments: 28 pages, 12 figures, 7 tables. Foundations of Data Science, Early Access, 2026
Journal ref: Foundations of Data Science, 11, 121-149 (2026)
DOI: 10.3934/fods.2026005
Code: https://github.com/ahxmeds/DAWN-FM
License: http://creativecommons.org/licenses/by/4.0/
The gist: Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing.
Terminology
Abstract
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization techniques to stabilize the solution. In this work, we employ Flow Matching (FM), a generative framework that integrates a deterministic processes to map a simple reference distribution, such as a Gaussian, to the target distribution. Our method DAWN-FM: Data-AWare and Noise-Informed Flow Matching incorporates data and noise embedding, allowing the model to access representations about the measured data explicitly and also account for noise in the observations, making it particularly robust in scenarios where data is noisy or incomplete. By learning a time-dependent velocity field, FM not only provides accurate solutions but also enables uncertainty quantification by generating multiple plausible outcomes. Unlike pretrained diffusion models, which may struggle in highly ill-posed settings, our approach is trained specifically for each inverse problem and adapts to varying noise levels. We validate the effectiveness and robustness of our method through extensive numerical experiments on tasks such as image deblurring and tomography. The code is available at: https://github.com/ahxmeds/DAWN-FM.git.
Sources
- Distributed Tikhonov regularization for ill-posed inverse problems from a Bayesian perspective
- Flow Matching for Generative Modeling
- Building Normalizing Flows with Stochastic Interpolants
- Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
- Diffusion Posterior Sampling for General Noisy Inverse Problems
- DRIP: Deep Regularizers for Inverse Problems
- Guided Flows for Generative Modeling and Decision Making
- D-Flow: Differentiating through Flows for Controlled Generation
- Training-free Linear Image Inverses via Flows
- Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
- The inverse crime
- U-Net: Convolutional Networks for Biomedical Image Segmentation
- Adam: A Method for Stochastic Optimization
Related papers
- PanoDiff-SR: Synthesizing Dental Panoramic Radiographs using Diffusion and Super-resolution
- Revisiting Integration of Image and Metadata for DICOM Series Classification: Cross-Attention and Dictionary Learning
- VesselSDF: Distance Field Priors for Vascular Network Reconstruction
- cSVR: Convolutional Slice-to-Volume Reconstruction
- NAIMA: Semantics Aware RGB Guided Depth Super-Resolution
- AneumoBench: A Source-Linked Benchmark for Synthetic-Geometry Transfer in Aneurysm CFD