DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems

arXiv:2412.04766 · eess.IV, cs.AI, cs.CV, cs.LG · Submitted 2026-02-28 · Read on arXiv

Shadab Ahamed, Eldad Haber

eess.IV, cs.AI, cs.CV, cs.LG

Submitted: 2026-02-28

Updated: 2026-08-19

Code: https://github.com/ahxmeds/DAWN-FM

Terminology

• Inverse Problem — 75× in this paper · explained in 2 episodes
• Flow Matching — 34× in this paper · explained in 8 episodes
• Diffusion Model — 16× in this paper · explained in 8 episodes
• Diffusion Models — 11× in this paper · explained in 6 episodes
• Regularization — 11× in this paper · explained in 3 episodes
• Adam — 7× in this paper · explained in 2 episodes
• Consistency — 6× in this paper · explained in 3 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Generative Model — 4× in this paper · explained in 2 episodes
• Generative Models — 4× in this paper · explained in 2 episodes
• Loss Function — 4× in this paper · explained in 2 episodes
• Mean Squared Error — 4× in this paper
• Peak Signal-to-Noise Ratio — 4× in this paper
• Fidelity — 3× in this paper · explained in 2 episodes
• Generative Modeling — 3× in this paper · explained in 3 episodes
• Structural Similarity Index Measure — 3× in this paper
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• Antithetic sampling — 2× in this paper · explained in 1 episode
• Canadian Institutes of Health Research — 2× in this paper
• Core — 2× in this paper · explained in 2 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Stochastic Interpolation — 2× in this paper
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Diffusion Process — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Feature Extraction — 1× in this paper · explained in 2 episodes
• Gaussian Point Spread Function — 1× in this paper
• Grounding — 1× in this paper · explained in 3 episodes
• Hybrid Approach — 1× in this paper · explained in 4 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Latent Representations — 1× in this paper · explained in 3 episodes
• Normalizing Flow — 1× in this paper · explained in 3 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Rectified Flow — 1× in this paper · explained in 3 episodes
• Synthetic Data Generation — 1× in this paper · explained in 5 episodes

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

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