# FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems

arXiv: https://arxiv.org/abs/2503.08136 · HTML: https://mlsanity.com/paper/2503.08136/

## Key facts

- Cited by 68 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [Regularization by Texts for Latent Diffusion Inverse Solvers](https://mlsanity.com/paper/2311.15658/) (2023)
- [DreamSampler: Unifying Diffusion Sampling and Score Distillation for Image Manipulation](https://mlsanity.com/paper/2403.11415/) (2024)

## Built on by (most cited first, 30 of 68)

- [Flower: A Flow-Matching Solver for Inverse Problems](https://mlsanity.com/paper/2509.26287/) (2025)
- [Solving Inverse Problems with FLAIR](https://mlsanity.com/paper/2506.02680/) (2025)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistency](https://mlsanity.com/paper/2602.18735/) (2026)
- [Chain-of-Zoom: Extreme Super-Resolution via Scale Autoregression and Preference Alignment](https://mlsanity.com/paper/2505.18600/) (2025)
- [ESS-Flow: Training-free guidance of flow-based models as inference in source space](https://mlsanity.com/paper/2510.05849/) (2025)
- [InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problem](https://mlsanity.com/paper/2512.05672/) (2025)
- [FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solvers](https://mlsanity.com/paper/2512.07150/) (2025)
- [D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching](https://mlsanity.com/paper/2602.21469/) (2026)
- [OmniGuide: Universal Guidance Fields for Enhancing Generalist Robot Policies](https://mlsanity.com/paper/2603.10052/) (2026)
- [Safety-Guided Flow (SGF): A Unified Framework for Negative Guidance in Safe Generation](https://mlsanity.com/paper/2603.13300/) (2026)
- [How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance](https://mlsanity.com/paper/2604.27147/) (2026)
- [Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidance](https://mlsanity.com/paper/2512.18365/) (2025)
- [ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Control](https://mlsanity.com/paper/2602.22742/) (2026)
- [Variational Flow Maps: Make Some Noise for One-Step Conditional Generation](https://mlsanity.com/paper/2603.07276/) (2026)
- [Conditional Flow Matching for Bayesian Posterior Inference](https://mlsanity.com/paper/2510.09534/) (2025)
- [SONIC: Spectral Optimization of Noise for Inpainting with Consistency](https://mlsanity.com/paper/2511.19985/) (2025)
- [FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problems](https://mlsanity.com/paper/2508.00721/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [Adaptive Weighted h-Transform Sampling for Coarse-Guided Visual Generation](https://mlsanity.com/paper/2603.12057/) (2026)
- [Trajectory Stitching for Solving Inverse Problems with Flow-Based Models](https://mlsanity.com/paper/2602.08538/) (2026)
- [A Stability Benchmark of Generative Regularizers for Inverse Problems](https://mlsanity.com/paper/2605.10076/) (2026)
- [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026)
- [Stitched Value Model for Diffusion Alignment](https://mlsanity.com/paper/2605.19804/) (2026)
- [Garment Particles: A 2D--3D Symmetric Garment Representation for Generation and Editing](https://mlsanity.com/paper/2605.26391/) (2026)
- [The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems](https://mlsanity.com/paper/2606.04804/) (2026)
- [Exact Posterior Score Estimation for Solving Linear Inverse Problems](https://mlsanity.com/paper/2606.17048/) (2026)
- [NullFlow: One-Step Generative Reconstruction](https://mlsanity.com/paper/2606.22696/) (2026)
- [Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers](https://mlsanity.com/paper/2601.04791/) (2026)
- [Solving Inverse Problems with Flow-based Models via Model Predictive Control](https://mlsanity.com/paper/2601.23231/) (2026)

## 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.