# Learning Efficient and Effective Trajectories for Differential Equation-based Image Restoration

arXiv: https://arxiv.org/abs/2410.04811 · HTML: https://mlsanity.com/paper/2410.04811/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 116 of its 160 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 116)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)

## Built on by (most cited first, 5 of 5)

- [Dark-EvGS: Event Camera as an Eye for Radiance Field in the Dark](https://mlsanity.com/paper/2507.11931/) (2025)
- [PixRestore: Unified Image Restoration via Pixel Diffusion Transformer](https://mlsanity.com/paper/2608.16793/) (2026)
- [Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models](https://mlsanity.com/paper/2604.10983/) (2026)
- [Enhancing Underwater Light Field Images via Global Geometry-aware Diffusion Process](https://mlsanity.com/paper/2601.21179/) (2026)
- [Mining Multi-Modality Spatio-Temporal Cues for Video Important Person Identification](https://mlsanity.com/paper/2605.28604/) (2026)

## Abstract (arXiv)

The differential equation-based image restoration approach aims to establish learnable trajectories connecting high-quality images to a tractable distribution, e.g., low-quality images or a Gaussian distribution. In this paper, we reformulate the trajectory optimization of this kind of method, focusing on enhancing both reconstruction quality and efficiency. Initially, we navigate effective restoration paths through a reinforcement learning process, gradually steering potential trajectories toward the most precise options. Additionally, to mitigate the considerable computational burden associated with iterative sampling, we propose cost-aware trajectory distillation to streamline complex paths into several manageable steps with adaptable sizes. Moreover, we fine-tune a foundational diffusion model (FLUX) with 12B parameters by using our algorithms, producing a unified framework for handling 7 kinds of image restoration tasks. Extensive experiments showcase the textitsignificant superiority of the proposed method, achieving a maximum PSNR improvement of 2.1 dB over state-of-the-art methods, while also greatly enhancing visual perceptual quality. Project page: https://zhu-zhiyu.github.io/FLUX-IR/.