mlsanityData to 7 Oct 2026

FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems

arXiv 2503.08136 ↗First posted 11 Mar 2025cs.CV cs.AI cs.LGcited by 65

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

Abstract (arXiv)

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Key facts. Cited by 65 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 24 of its 27 references that are in the map. First posted on arXiv 11 Mar 2025.

Builds on

24 of 27 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generation27 Nov
  2. 2022Flow Matching for Generative Modeling6 Oct
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 21

  1. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2023Visual Instruction Tuningcited by 7,792
  5. 2022Scalable Diffusion Models with Transformerscited by 5,931
  6. 2022Classifier-Free Diffusion Guidancecited by 5,717
  7. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,131
  8. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  9. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  11. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 574
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
9 more
  1. 2023SeeSR: Towards Semantics-Aware Real-World Image Super-Resolutioncited by 311
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  5. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 129
  6. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  7. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  8. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 31
  9. 2024DreamSampler: Unifying Diffusion Sampling and Score Distillation for Image Manipulationcited by 22

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 14; 2026: 51.

65 papers.

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  1. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  2. 2025Solving Inverse Problems with FLAIRcited by 16
  3. 2025Diffusion models for inverse problemscited by 15
  4. 2026LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistencycited by 9
  5. 2025Chain-of-Zoom: Extreme Super-Resolution via Scale Autoregression and Preference Alignmentcited by 8
  6. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  7. 2025InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problemcited by 6
  8. 2026OmniGuide: Universal Guidance Fields for Enhancing Generalist Robot Policiescited by 6
  9. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  10. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  11. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  12. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generationcited by 5
38 more
  1. 2026How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidancecited by 5
  2. 2025SONIC: Spectral Optimization of Noise for Inpainting with Consistencycited by 4
  3. 2026ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Controlcited by 4
  4. 2026Safety-Guided Flow (SGF): A Unified Framework for Negative Guidance in Safe Generationcited by 4
  5. 2025FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problemscited by 3
  6. 2025Conditional Flow Matching for Bayesian Posterior Inferencecited by 3
  7. 2026DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstructioncited by 3
  8. 2026Adaptive Weighted h-Transform Sampling for Coarse-Guided Visual Generationcited by 3
  9. 2026Image Restoration via Diffusion Models with Dynamic Resolutioncited by 2
  10. 2026Stitched Value Model for Diffusion Alignmentcited by 2
  11. 2026Garment Particles: A 2D--3D Symmetric Garment Representation for Generation and Editingcited by 2
  12. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  13. 2026Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solverscited by 1
  14. 2026Solving Inverse Problems with Flow-based Models via Model Predictive Controlcited by 1
  15. 2026Trajectory Stitching for Solving Inverse Problems with Flow-Based Modelscited by 1
  16. 2026PASDiff: Physics-Aware Semantic Guidance for Joint Real-World Low-Light Face Enhancement and Restorationcited by 1
  17. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 1
  18. 2026FlowLong: Inference-time Long Video Generation via Manifold-constrained Tweedie Matchingcited by 1
  19. 2026The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problemscited by 1
  20. 2026Exact Posterior Score Estimation for Solving Linear Inverse Problemscited by 1
  21. 2026What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport Viewcited by 1
  22. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributionscited by 0
  23. 2025Null-Space Diffusion Distillation Unlocks Speed, Fidelity and Realism in Lensless Imagingcited by 0
  24. 2025Saving Foundation Flow-Matching Priors for Inverse Problemscited by 0
  25. 2026MPFlow: Multi-modal Posterior-Guided Flow Matching for Zero-Shot MRI Reconstructioncited by 0
  26. 2026Beyond Fixed Inference: Quantitative Flow Matching for Adaptive Image Denoisingcited by 0
  27. 2026FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priorscited by 0
  28. 2026Guided Streaming Stochastic Interpolant Policycited by 0
  29. 2026Accelerating Video Inverse Problem Solvers with Autoregressive Diffusion Modelscited by 0
  30. 2026Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse Problems: Optimizing Guidance and Stochasticity Schedulescited by 0
  31. 2026A Unified Two-Stage Generative Diffusion Framework for Channel Estimation and Port Selection in Multiuser MIMO-FAScited by 0
  32. 2026FlowBender: Feedback-Aware Training for Self-Correcting Conditional Flowscited by 0
  33. 2026Stochastic Optimal Control Sampling for Diffusion Inverse Problemscited by 0
  34. 2026DICT: Data Injection and Contrastive Trajectory Refinement for Conditional Image Generation with Diffusion Modelscited by 0
  35. 2026Posterior Samplings are Missing Modalities Generators for Medical Image Translationcited by 0
  36. 2026Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matchingcited by 0
  37. 2026Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Modelscited by 0
  38. 2026Making Every Step Count: Spatio-Temporal Information Allocation for Imaging Inverse Problemscited by 0

50 most cited of 65 All 65 (JSON)

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  1. 2023Training-free Linear Image Inverses via Flows
  2. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
  3. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching
  4. 2026P-Flow: Proxy-gradient Flows for Linear Inverse Problems
  5. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  6. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
  7. 2024Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching
  8. 2024DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems