# Implicit Image-to-Image Schrodinger Bridge for Image Restoration

arXiv: https://arxiv.org/abs/2403.06069 · HTML: https://mlsanity.com/paper/2403.06069/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 30 of 37)

- [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)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [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)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [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)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [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)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)

## Built on by (most cited first, 14 of 14)

- [Diffusion Bridge Implicit Models](https://mlsanity.com/paper/2405.15885/) (2024)
- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Inverse Bridge Matching Distillation](https://mlsanity.com/paper/2502.01362/) (2025)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [Sample from What You See: Visuomotor Policy Learning via Diffusion Bridge with Observation-Embedded Stochastic Differential Equation](https://mlsanity.com/paper/2512.07212/) (2025)
- [A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2505.21528/) (2025)
- [Probabilistic Super-Resolution for Urban Micrometeorology via a Schr"odinger Bridge](https://mlsanity.com/paper/2510.12148/) (2025)
- [Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models](https://mlsanity.com/paper/2604.10983/) (2026)
- [Semantic Granularity Navigation in Image Editing](https://mlsanity.com/paper/2605.21190/) (2026)
- [SURE Guided Posterior Sampling: Trajectory Correction for Diffusion-Based Inverse Problems](https://mlsanity.com/paper/2512.23232/) (2025)
- [Unifying Deep Stochastic Processes for Image Enhancement](https://mlsanity.com/paper/2605.01568/) (2026)
- [Resolving Endpoint Underfitting in Diffusion Bridges via Noise Alignment](https://mlsanity.com/paper/2605.28962/) (2026)
- [GoodDiffusion: Proactive Copyright Protection for Diffusion Bridge Models via Learnable Sample-specific Signatures](https://mlsanity.com/paper/2606.29759/) (2026)
- [PRISM: Principled Reference Identification for Schrodinger Bridge Model](https://mlsanity.com/paper/2608.06893/) (2026)

## Abstract (arXiv)

Diffusion-based models have demonstrated remarkable effectiveness in image restoration tasks; however, their iterative denoising process, which starts from Gaussian noise, often leads to slow inference speeds. The Image-to-Image Schr"odinger Bridge (I2SB) offers a promising alternative by initializing the generative process from corrupted images while leveraging training techniques from score-based diffusion models. In this paper, we introduce the Implicit Image-to-Image Schr"odinger Bridge (I3SB) to further accelerate the generative process of I2SB. I3SB restructures the generative process into a non-Markovian framework by incorporating the initial corrupted image at each generative step, effectively preserving and utilizing its information. To enable direct use of pretrained I2SB models without additional training, we ensure consistency in marginal distributions. Extensive experiments across many image corruptions, including noise, low resolution, JPEG compression, and sparse sampling, and multiple image modalities, such as natural, human face, and medical images, demonstrate the acceleration benefits of I3SB. Compared to I2SB, I3SB achieves the same perceptual quality with fewer generative steps, while maintaining or improving fidelity to the ground truth.