# Saving Foundation Flow-Matching Priors for Inverse Problems

arXiv: https://arxiv.org/abs/2511.16520 · HTML: https://mlsanity.com/paper/2511.16520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 37 of its 55 references that are in the map.
- First posted on arXiv 20 Nov 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, 30 of 37)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [One-Step Effective Diffusion Network for Real-World Image Super-Resolution](https://mlsanity.com/paper/2406.08177/) (2024)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [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)
- [Pixel-level and Semantic-level Adjustable Super-resolution: A Dual-LoRA Approach](https://mlsanity.com/paper/2412.03017/) (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)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Solving Inverse Problems with FLAIR](https://mlsanity.com/paper/2506.02680/) (2025)
- [Self-Validation: Early Stopping for Single-Instance Deep Generative Priors](https://mlsanity.com/paper/2110.12271/) (2021)
- [Comparing the Robustness of Modern No-Reference Image- and Video-Quality Metrics to Adversarial Attacks](https://mlsanity.com/paper/2310.06958/) (2023)
- [Learning Transferable Features for Implicit Neural Representations](https://mlsanity.com/paper/2409.09566/) (2024)

## Abstract (arXiv)

Foundation flow-matching (FM) models promise universal priors for solving inverse problems (IPs); yet today, they trail behind domain-specific and even untrained priors. How can we unlock their potential? We introduce FMPlug, a plug-in framework that redefines how foundation FMs are used in IPs. FMPlug combines an instance-guided, time-dependent warm-start strategy with sharp Gaussianity regularization, adding problem-specific guidance while preserving the Gaussian structures. For evaluation, we consider both simple image restoration tasks and scientific IPs with a few similar samples -- where the prohibitive cost of data collection and model training hinders the development of domain-specific generative models. Our superior experimental results confirm the effectiveness of FMPlug. Overall, FMPlug paves the way for making foundation FM models practical, reusable priors for IPs, especially scientific ones with few similar samples. More details are available at https://sun-umn.github.io/xm-plug/ .