mlsanityData to 7 Oct 2026

Flower: A Flow-Matching Solver for Inverse Problems

arXiv 2509.26287 ↗First posted 30 Sep 2025cs.CV cs.LGcited by 23

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps: (i) a flow-consistent destination estimation, where the velocity network predicts a denoised target; (ii) a refinement step that projects the estimated destination onto a feasible set defined by the forward operator; and (iii) a time-progression step that re-projects the refined destination along the flow trajectory. We provide a theoretical analysis that demonstrates how Flower approximates Bayesian posterior sampling, thereby unifying perspectives from plug-and-play methods and generative inverse solvers. On the practical side, Flower achieves state-of-the-art reconstruction quality while using nearly identical hyperparameters across various linear inverse problems. Our code is available at https://github.com/mehrsapo/Flower.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 33 of its 43 references that are in the map. First posted on arXiv 30 Sep 2025.

Builds on

33 of 43 references.

Closest ancestors · 9

Same direction, newest first

  1. 2025Solving Inverse Problems with FLAIR3 Jun
  2. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems11 Mar
  3. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching29 May
  4. 2024D-Flow: Differentiating through Flows for Controlled Generation21 Feb
  5. 2023Training-free Linear Image Inverses via Flows25 Sep
  6. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  7. 2022Flow Matching for Generative Modeling6 Oct
  8. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 24

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  7. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  8. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  9. 2022Denoising Diffusion Restoration Modelscited by 951
  10. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  11. 2014Convex Optimization: Algorithms and Complexitycited by 569
  12. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
12 more
  1. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  2. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  4. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 129
  5. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  6. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  7. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  8. 2015From Facial Parts Responses to Face Detection: A Deep Learning Approachcited by 42
  9. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  10. 2023Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithmscited by 30
  11. 2025DEALing with Image Reconstruction: Deep Attentive Least Squarescited by 6
  12. 2024Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstructioncited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 22.

23 papers.

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  1. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  2. 2026Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoisercited by 2
  3. 2026Conditional flow matching for physics-constrained inverse problems with finite training datacited by 2
  4. 2026FluxFlow: Conservative Flow-Matching for Astronomical Image Super-Resolutioncited by 2
  5. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  6. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 1
  7. 2026What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport Viewcited by 1
  8. 2026Efficient Flow Matching for Sparse-View CT Reconstructioncited by 0
  9. 2026P-Flow: Proxy-gradient Flows for Linear Inverse Problemscited by 0
  10. 2026FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priorscited by 0
  11. 2026Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse Problems: Optimizing Guidance and Stochasticity Schedulescited by 0
  12. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
11 more
  1. 2026Constrained Flow Matching via Lagrangian Dual Flowscited by 0
  2. 2026Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matchingcited by 0
  3. 2026Making Every Step Count: Spatio-Temporal Information Allocation for Imaging Inverse Problemscited by 0
  4. 2026Flow Matching-Based PET Image Reconstructioncited by 0
  5. 2026Physics-Guided Flow Matching for CT Image Reconstructioncited by 0
  6. 2026SurfSpec: Enhancing Off-Target-Agnostic Specificity by Bounding Pocket-Ligand Geometric Mismatchcited by 0
  7. 2026ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Frontcited by 0
  8. 2026Fast and Faithful: Principled Conditional Flow Matching for Inverse Problemscited by 0
  9. 2026CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flowcited by 0
  10. 2026SNaP: One-Step Posterior Sampling for Noisy Inverse Problemscited by 0
  11. 2026Principled MAP estimation for inverse problems: bridging the gap between convergence and performancecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
  2. 2026FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants
  3. 2024DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems
  4. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  5. 2026Training-Free Refinement of Flow Matching with Divergence-based Sampling
  6. 2025FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problems
  7. 2026Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
  8. 2025Multi Task Denoiser Training for Solving Linear Inverse Problems ↗