# γ-Bridge: A Look-Parametric Diffusion Bridge

arXiv: https://arxiv.org/abs/2607.22719 · HTML: https://mlsanity.com/paper/2607.22719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [Diffusion Bridge Implicit Models](https://mlsanity.com/paper/2405.15885/) (2024)
- [SAR image despeckling through convolutional neural networks](https://mlsanity.com/paper/1704.00275/) (2017)
- [Speckle2Void: Deep Self-Supervised SAR Despeckling with Blind-Spot Convolutional Neural Networks](https://mlsanity.com/paper/2007.02075/) (2020)
- [Diffusion Model for Generative Image Denoising](https://mlsanity.com/paper/2302.02398/) (2023)
- [Denoising Diffusion Gamma Models](https://mlsanity.com/paper/2110.05948/) (2021)
- [SAR Image Despeckling Using a Convolutional Neural Network](https://mlsanity.com/paper/1706.00552/) (2017)
- [SAR Despeckling using a Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2206.04514/) (2022)
- [As if by magic: self-supervised training of deep despeckling networks with MERLIN](https://mlsanity.com/paper/2110.13148/) (2021)
- [Transformer-based SAR Image Despeckling](https://mlsanity.com/paper/2201.09355/) (2022)
- [Residual Diffusion Bridge Model for Image Restoration](https://mlsanity.com/paper/2510.23116/) (2025)
- [Star-Shaped Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.05259/) (2023)
- [Generalized Consistency Trajectory Models for Image Manipulation](https://mlsanity.com/paper/2403.12510/) (2024)
- [SDDPM: Speckle Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2311.10868/) (2023)
- [SAR Despeckling via Regional Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2401.03122/) (2024)
- [Towards Deep Unsupervised SAR Despeckling with Blind-Spot Convolutional Neural Networks](https://mlsanity.com/paper/2001.05264/) (2020)
- [A Tunable Despeckling Neural Network Stabilized via Diffusion Equation](https://mlsanity.com/paper/2411.15921/) (2024)
- [Self-Supervised Score-Based Despeckling for SAR Imagery via Log-Domain Transformation](https://mlsanity.com/paper/2601.14334/) (2026)

## Abstract (arXiv)

Multiplicative Gamma noise is a signal-dependent degradation in coherent imaging; synthetic aperture radar (SAR) despeckling is its most prominent real-world instance. Existing diffusion denoisers parameterize their forward process by abstract signal-to-noise schedules rather than by the physical look number L, so different deployment scenarios typically require separately trained models, and transfer from synthetic Gamma training to real SAR remains challenging without clean ground truth. We introduce γ-Bridge, a look-parametric bridge whose schedule L(t) connects the noisy observation at Lobs to the clean limit through exact multiplicative Gamma marginals. Its closed-form Gamma--L'evy reverse posterior admits both stochastic and deterministic processes, while observation conditioning and a two-step consistency loss stabilize multi-step inference in the low-SNR single-look regime. Because bridge time directly represents L, one conditioned network can smart-start from any admissible input look and stop at a target look number. These two orthogonal controls enable zero-shot restoration over the full admissible grid after training only at Lobs = 1 on natural images with synthetic Gamma corruption. Combined with a homogeneous-patch look estimator, γ-Bridge processes data from six spaceborne and airborne SAR sensors without sensor-specific fine-tuning, achieving leading results on standard synthetic benchmarks while providing physically interpretable input and output controls absent from prior denoisers. Codes are released hrefhttps://github.com/Teriri1999/GammaBridgehere.