# Self-Consistent Recursive Diffusion Bridge for Medical Image Translation

arXiv: https://arxiv.org/abs/2405.06789 · HTML: https://mlsanity.com/paper/2405.06789/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 42 of its 83 references that are in the map.
- First posted on arXiv 10 May 2024.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 30 of 42)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Unsupervised Medical Image Translation with Adversarial Diffusion Models](https://mlsanity.com/paper/2207.08208/) (2022)
- [ResViT: Residual vision transformers for multi-modal medical image synthesis](https://mlsanity.com/paper/2106.16031/) (2021)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [MedGAN: Medical Image Translation using GANs](https://mlsanity.com/paper/1806.06397/) (2018)
- [Image Synthesis in Multi-Contrast MRI with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1802.01221/) (2018)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Missing MRI Pulse Sequence Synthesis using Multi-Modal Generative Adversarial Network](https://mlsanity.com/paper/1904.12200/) (2019)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [Deep MR to CT Synthesis using Unpaired Data](https://mlsanity.com/paper/1708.01155/) (2017)
- [Hi-Net: Hybrid-fusion Network for Multi-modal MR Image Synthesis](https://mlsanity.com/paper/2002.05000/) (2020)
- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [Conversion Between CT and MRI Images Using Diffusion and Score-Matching Models](https://mlsanity.com/paper/2209.12104/) (2022)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [Unified Multi-Modal Image Synthesis for Missing Modality Imputation](https://mlsanity.com/paper/2304.05340/) (2023)
- [Self-Supervised MRI Reconstruction with Unrolled Diffusion Models](https://mlsanity.com/paper/2306.16654/) (2023)
- [DiamondGAN: Unified Multi-Modal Generative Adversarial Networks for MRI Sequences Synthesis](https://mlsanity.com/paper/1904.12894/) (2019)

## Built on by (most cited first, 26 of 26)

- [I2I-Mamba: Multi-modal medical image synthesis via selective state space modeling](https://mlsanity.com/paper/2405.14022/) (2024)
- [DenoMamba: A fused state-space model for low-dose CT denoising](https://mlsanity.com/paper/2409.13094/) (2024)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [Regression is all you need for medical image translation](https://mlsanity.com/paper/2505.02048/) (2025)
- [Physics-Inspired Generative Models in Medical Imaging: A Review](https://mlsanity.com/paper/2407.10856/) (2024)
- [Back-in-Time Diffusion: Unsupervised Detection of Medical Deepfakes](https://mlsanity.com/paper/2407.15169/) (2024)
- [Generative Autoregressive Transformers for Model-Agnostic Federated MRI Reconstruction](https://mlsanity.com/paper/2502.04521/) (2025)
- [Learning Modality-Aware Representations: Adaptive Group-wise Interaction Network for Multimodal MRI Synthesis](https://mlsanity.com/paper/2411.14684/) (2024)
- [Virtual Full-stack Scanning of Brain MRI via Imputing Any Quantised Code](https://mlsanity.com/paper/2501.18328/) (2025)
- [Adaptive Domain Shift in Diffusion Models for Cross-Modality Image Translation](https://mlsanity.com/paper/2601.18623/) (2026)
- [Contrast-X: A Multi-Modal Contrast Image Synthesis Benchmark and Universal Modality Flow Matching](https://mlsanity.com/paper/2601.15884/) (2026)
- [Unpaired Image-to-Image Translation via a Self-Supervised Semantic Bridge](https://mlsanity.com/paper/2602.16664/) (2026)
- [Self-Consistent Nested Diffusion Bridge for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2412.09998/) (2024)
- [Meta-Entity Driven Triplet Mining for Aligning Medical Vision-Language Models](https://mlsanity.com/paper/2504.15929/) (2025)
- [BronchoGAN: Anatomically consistent and domain-agnostic image-to-image translation for video bronchoscopy](https://mlsanity.com/paper/2507.01387/) (2025)
- [Uncertainty-Aware Distribution-to-Distribution Flow Matching for Scientific Imaging](https://mlsanity.com/paper/2603.21717/) (2026)
- [Principled Feature Disentanglement for High-Fidelity Unified Brain MRI Synthesis](https://mlsanity.com/paper/2406.14954/) (2024)
- [Path and Bone-Contour Regularized Unpaired MRI-to-CT Translation](https://mlsanity.com/paper/2505.03114/) (2025)
- [Predicting before Reconstruction: A generative prior framework for MRI acceleration](https://mlsanity.com/paper/2510.19472/) (2025)
- [Recover Semantics First, Generate Better: Improved Latent Modeling for 3D MRI Reconstruction and Cross-Contrast Synthesis](https://mlsanity.com/paper/2606.17989/) (2026)
- [Prob-BBDM: a Probabilistic Brownian Bridge Diffusion Model for MRI sequence image-to-image translation](https://mlsanity.com/paper/2606.24313/) (2026)
- [Do Not Break the Vessels: Structure-Preserving Mean Flow for Vascular Image Translation](https://mlsanity.com/paper/2606.31095/) (2026)
- [Heterogeneity-Adaptive Diffusion Schrodinger Bridge for PET-Guided Whole-Body MRI Translation](https://mlsanity.com/paper/2607.07401/) (2026)
- [Posterior Samplings are Missing Modalities Generators for Medical Image Translation](https://mlsanity.com/paper/2607.18763/) (2026)
- [VeCAS: Vessel-Focused Contrast-Free Angiogram Synthesis for Vascular Interventions](https://mlsanity.com/paper/2608.22828/) (2026)
- [PredRA: Fast Medical Image Translation by Deterministic Component Extraction and Controlled Stochastic Refinement](https://mlsanity.com/paper/2609.31912/) (2026)

## Abstract (arXiv)

Denoising diffusion models (DDM) have gained recent traction in medical image translation given improved training stability over adversarial models. DDMs learn a multi-step denoising transformation to progressively map random Gaussian-noise images onto target-modality images, while receiving stationary guidance from source-modality images. As this denoising transformation diverges significantly from the task-relevant source-to-target transformation, DDMs can suffer from weak source-modality guidance. Here, we propose a novel self-consistent recursive diffusion bridge (SelfRDB) for improved performance in medical image translation. Unlike DDMs, SelfRDB employs a novel forward process with start- and end-points defined based on target and source images, respectively. Intermediate image samples across the process are expressed via a normal distribution with mean taken as a convex combination of start-end points, and variance from additive noise. Unlike regular diffusion bridges that prescribe zero variance at start-end points and high variance at mid-point of the process, we propose a novel noise scheduling with monotonically increasing variance towards the end-point in order to boost generalization performance and facilitate information transfer between the two modalities. To further enhance sampling accuracy in each reverse step, we propose a novel sampling procedure where the network recursively generates a transient-estimate of the target image until convergence onto a self-consistent solution. Comprehensive analyses in multi-contrast MRI and MRI-CT translation indicate that SelfRDB offers superior performance against competing methods.