γ-Bridge

A Look-Parametric Diffusion Bridge

Official implementation of γ-Bridge: A Look-Parametric Diffusion Bridge.

γ-Bridge indexes a diffusion bridge by the physical look number rather than an abstract noise schedule. Every intermediate state along the bridge is a physically valid look parametric image with exact Gamma marginals, and a closed-form Gamma–Lévy reverse posterior admits both stochastic and deterministic updates. Combined with observation conditioning and a two-step consistency loss, a single network trained on natural images with synthetic single-look corruption performs zero-shot restoration across a range of input/output look numbers and transfers to spaceborne and airborne SAR sensors without sensor-specific fine-tuning.

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Runtime Controls

Two orthogonal controls at inference, both without retraining:

• Target-look output  — terminate the reverse chain at any desired output look number to obtain a calibrated multi-look image with matching Gamma statistics.
• Smart-start input  — anchor an observation with an estimated effective look number to the matching bridge step and run the reverse chain from there.

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Repository Layout

gamma-bridge/
├── train.py                  synthetic training (BSDS500 + DIV2K, DDP-ready)
├── sample.py                 multi-step reverse with optional target-L
├── requirements.txt
├── gbridge_core/
│   ├── diffusion.py          GammaBridge: forward q, closed-form Levy posterior
│   ├── network.py            UNet + log-L conditioning
│   └── gd/                   guided-diffusion UNet blocks
├── models/gamma_bridge.py    exact Gamma forward kernel + L(t) schedule
├── data/                     BSDS500 loaders + downloader
├── eval/                     PSNR / SSIM / ratio-statistic evaluation
├── figures/                  paper-figure reproduction scripts
├── scripts/                  ablation and control helpers
├── tests/                    pytest unit tests
└── assets/                   paper-figure PNGs

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Installation

conda create -n gbridge python=3.10 -y
conda activate gbridge

pip install -r requirements.txt
pip install torch torchvision --index-url https://download.pytorch.org/whl/cu121

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Pretrained Model

The flagship checkpoint used in the paper is attached to the v1.0.0 release.

mkdir -p weights
wget -O weights/gbridge_L1.pt \
    https://github.com/Teriri1999/GammaBridge/releases/download/v1.0.0/gbridge_L1.pt

Trained on BSDS500 + DIV2K natural images for 15,000 steps with the flagship configuration below.

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Data

Training uses BSDS500 train+val and DIV2K train HR natural images (~1,100 crops of 256 × 256) with synthetic single-look Gamma corruption. No real SAR imagery is used during training.

# BSDS500 is fetched automatically on first dataloader init, or manually:
python -m data.download_bsds500

# DIV2K HR (~3.4 GB):
mkdir -p data/downloads data/div2k
wget http://data.vision.ee.ethz.ch/cvl/DIV2K/DIV2K_train_HR.zip -P data/downloads
unzip data/downloads/DIV2K_train_HR.zip -d data/div2k

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Training

The paper's flagship configuration (100-step log schedule spanning single-look to near-clean; loss weights (rec, ratio, cons) = (10, 1, 5); deterministic defaults; a fully convolutional UNet with 64 base channels and (1, 2, 4) multipliers):

python train.py \
    --L_obs 1.0 --T 100 --L_max 10000 --schedule log \
    --image_size 256 --model_channels 64 \
    --bridge_forward --cond_x1 \
    --lambda_rec 10 --lambda_ratio 1 --lambda_consistency 5 \
    --batch_size 2 --total_steps 15000 \
    --lr_G 1e-4 --ema_decay 0.999 \
    --extra_roots data/div2k/DIV2K_train_HR \
    --out_dir checkpoints/gbridge

Multi-GPU:

torchrun --nproc_per_node=4 train.py [...same flags...]

Key flags (python train.py --help for the full list):

Flag	Meaning
--L_obs, --L_max, --T	bridge endpoints and step count
--schedule	log or linear interpolation of the look-number schedule
--bridge_forward	use the Gamma–Lévy bridge forward process
--cond_x1	pass the observation as a second input channel
--lambda_rec / _ratio / _consistency	loss weights
--direct_pred	ablation: linear-residual head
--naive_posterior	ablation: skip the Lévy posterior
--extra_roots	extra image folders (e.g. DIV2K HR) added to the training pool

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Evaluation

BSDS500 test set:

python eval/run_eval.py \
    --ckpt path/to/ckpt.pt \
    --num_samples 64 --num_steps 6 --ot_ode \
    --out_csv eval/results/gbridge_ns6.csv

Reports PSNR, SSIM, ratio-image mean & variance, and a Kolmogorov–Smirnov p-value against the reference Gamma distribution.

External synthetic benchmarks (Set12 / Kodak24 / McMaster / BSDS100):

python eval/run_external.py --ckpt path/to/ckpt.pt --dataset kodak24 --nfe 5 --ot_ode

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Sampling

# Full clean denoise
python sample.py --ckpt path/to/ckpt.pt --num_steps 6 --ot_ode

# Target-look output control
python sample.py --ckpt path/to/ckpt.pt --target_L 8 --num_steps 6 --ot_ode

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Real SAR

Trained purely on natural images with synthetic single-look corruption, γ-Bridge combines a homogeneous-patch look-number estimator with smart-start to process real SAR from six sensors — Sentinel-1, TerraSAR-X, Gaofen-3 (spaceborne); miniSAR, FARAD X-band, FARAD Ka-band (airborne) — without sensor-specific fine-tuning.

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Reproducing Paper Figures

python figures/viz_multistep.py --ckpt path/to/ckpt.pt --num_samples 8
python figures/viz_L_sweep.py   --ckpt path/to/ckpt.pt --num_samples 64 --nfe 5
python figures/viz_target_L.py  --ckpt path/to/ckpt.pt --num_samples 6

Citation

If you find this work useful, please cite:

@article{hu2026gamma,
  title={$$\backslash$gamma $-Bridge: A Look-Parametric Diffusion Bridge},
  author={Hu, Xuran and Zhu, Yujie and Wang, Tengxi and Li, Jilong and Zhao, Wufan},
  journal={arXiv preprint arXiv:2607.22719},
  year={2026}
}