γ-Bridge: A Look-Parametric Diffusion Bridge

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.