# FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solvers

arXiv: https://arxiv.org/abs/2512.07150 · HTML: https://mlsanity.com/paper/2512.07150/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 41 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [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)
- [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)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (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)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2503.08136/) (2025)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning](https://mlsanity.com/paper/2012.12137/) (2020)
- [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)

## Built on by (most cited first, 6 of 6)

- [Accelerating Video Inverse Problem Solvers with Autoregressive Diffusion Models](https://mlsanity.com/paper/2605.20624/) (2026)
- [Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse Problems: Optimizing Guidance and Stochasticity Schedules](https://mlsanity.com/paper/2605.26470/) (2026)
- [Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matching](https://mlsanity.com/paper/2608.00537/) (2026)
- [Making Every Step Count: Spatio-Temporal Information Allocation for Imaging Inverse Problems](https://mlsanity.com/paper/2608.11747/) (2026)
- [SurfSpec: Enhancing Off-Target-Agnostic Specificity by Bounding Pocket-Ligand Geometric Mismatch](https://mlsanity.com/paper/2609.02963/) (2026)
- [LyapuFlow: Controlling Generative Flows with Lyapunov Feedback for Inverse Problems](https://mlsanity.com/paper/2610.04326/) (2026)

## Abstract (arXiv)

Deep generative models are powerful priors for imaging inverse problems, but training-free solvers for latent flow models face a practical finite-step trade-off. Optimization-heavy methods quickly improve measurement consistency, but in highly nonlinear latent spaces, their results can depend strongly on where local refinement is initialized, often degrading perceptual realism. In contrast, stochastic sampling methods better preserve posterior exploration, but often require many iterations to obtain sharp, measurement-consistent reconstructions. To address this trade-off, we propose FlowLPS, a training-free latent flow inverse solver based on Langevin-Proximal Sampling. At each reverse step, FlowLPS uses a few Langevin updates to perturb the model-predicted clean estimate in posterior-oriented directions, providing stochastic initializations for local refinement. It then applies local MAP-style proximal refinement to rapidly improve measurement consistency from the Langevin-updated estimate. We additionally use controlled pCN-style re-noising to stabilize the reverse trajectory while retaining trajectory coherence. Experiments on FFHQ and DIV2K across five linear inverse problems show that FlowLPS achieves a strong balance between measurement fidelity and perceptual quality, with additional experiments on pixel-space inverse problems and phase retrieval.