# Efficient Image Restoration with State-Dependent Forward Diffusion

arXiv: https://arxiv.org/abs/2505.16733 · HTML: https://mlsanity.com/paper/2505.16733/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Deep Retinex Decomposition for Low-Light Enhancement](https://mlsanity.com/paper/1808.04560/) (2018)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shifting](https://mlsanity.com/paper/2307.12348/) (2023)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [FFA-Net: Feature Fusion Attention Network for Single Image Dehazing](https://mlsanity.com/paper/1911.07559/) (2019)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)

## Built on by (most cited first, 2 of 2)

- [Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis](https://mlsanity.com/paper/2509.24531/) (2025)
- [Disentangling Generation and Regression in Stochastic Interpolants for Controllable Image Restoration](https://mlsanity.com/paper/2605.21381/) (2026)

## Abstract (arXiv)

This paper proposes to perform image restoration through a state-dependent mean-reverting forward diffusion (FoD) process. In contrast to traditional diffusion-based approaches that rely on a coupled forward-backward diffusion scheme, FoD directly learns image restoration through a single forward diffusion process, yielding a simple yet efficient framework. The core of FoD is a state-dependent stochastic differential equation (SDE) that involves a mean-reverting term in both the drift and diffusion functions. This mean-reverting structure drives the low-quality data toward the clean endpoint with controlled stochastic variation, therefore simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling few-step sampling during inference. The proposed FoD model, despite its simplicity, achieves strong overall performance on various image restoration tasks compared to representative diffusion, diffusion bridge, and flow matching approaches. The code is available at https://github.com/Algolzw/FoD.