A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

Adversarial purification with diffusion models seeks to project adversarial examples back toward the data manifold, but balancing semantic preservation and robustness against adaptive attacks remains challenging. Recent work shows that standard diffusion purification can fail under adaptive evaluation, while test-time score-based optimization is more resilient. Existing optimization defenses, however, typically rely on a single diffusion noise regime or treat timesteps uniformly, overlooking the distinct roles of coarse and fine denoising scales. We propose Temporal Adversarial Rectification Optimization (TARO), an inference-time purification method that builds a temporally guided score prior from multiple denoising views along the diffusion trajectory. TARO forms a coarse-to-fine residual target: high-noise experts provide globally smoothed structure with reduced adversarial sensitivity, while low-noise experts restore image-specific, class-relevant details. A guidance strength controls this temporal correction, allowing TARO to balance robust global rectification with semantic preservation. Empirically, TARO improves robust accuracy across datasets and adaptive threat models in a zero-shot setting, while remaining compatible with complementary adversarial-likelihood objectives for further robustness gains.

Deep neural networks are vulnerable to adversarial perturbations, limiting deployment in safety-critical applications such as synthetic aperture radar (SAR) automatic target recognition (ATR). Randomized smoothing improves robustness by averaging predictions over noisy inputs, but isotropic noise often fails to preserve the semantic structure of SAR imagery. We propose semantic smoothing, a defense that replaces noised-based perturbations with structured randomized transformations generated by a novel view synthesis model. For SAR, we condition on acquisition geometry to synthesize multiple plausible radar views. Predictions across generated randomized views are aggregated to form a robust classifier. Experiments show that semantic smoothing improves robustness against standard attacks, such as FGSM and PGD, and SAR-specific attacks, such as OTSA and SMGAA, while also increasing clean classification accuracy. These results demonstrate that randomized smoothing via semantically preserving geometric transformations is a promising alternative to isotropic noise for adversarial defense in structured sensing domains.

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 $L_{obs}$ to the clean limit through exact multiplicative Gamma marginals. Its closed-form Gamma--Lévy 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 $L_{obs} = 1$ 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 \href{https://github.com/Teriri1999/GammaBridge}{here}.