Technical Summary: Backbone-Agnostic Perturbation-Induced Uncertainty Learning for End-to-End Real-World Image Dehazing

Problem Statement

Real-world image dehazing remains a challenging ill-posed problem due to the spatially non-uniform, illumination-dependent, and physically ambiguous nature of haze degradation. While existing end-to-end restoration networks typically formulate dehazing as a deterministic mapping from a hazy observation to a clean target, they often fail to explicitly explore the uncertainty hidden within degraded features, haze priors, and cross-domain negative samples. Even with paired real-world datasets (e.g., I-HAZE, O-HAZE, Dense-Haze), pixel-wise reconstruction alone can result in over-smoothed structures or color deviations because standard supervised learning does not account for the varying sensitivity of different feature channels and spatial locations to haze. Furthermore, existing methods often lack mechanisms to verify if a restored image is physically consistent with the observed haze formation process or to effectively separate clean targets from real and synthetic degradation domains in feature space.

Methodology: BPUL Framework

The authors propose Backbone-Agnostic Perturbation-Induced Uncertainty Learning (BPUL), a plug-and-play framework designed to model degradation-sensitive feature uncertainty without requiring a redesign of the underlying restoration backbone. BPUL consists of three complementary components:

1. Learnable Perturbation-induced Uncertainty Modulator (LPUM)

LPUM is the core inference-time module inserted into intermediate layers of a restoration backbone (CNN, Transformer, or hybrid). It operates by:

• Stochastic Perturbation: Injecting learnable stochastic perturbations into intermediate feature maps. It estimates channel-wise and spatial-wise perturbation distributions using reparameterized sampling (predicting mean and log-standard deviation).
• Uncertainty Response: Comparing the original feature response with the inverse-aligned perturbed response to compute a discrepancy map. This discrepancy measures the sensitivity of specific channels and spatial locations to haze-related perturbations.
• Feature Modulation: Converting these discrepancies into modulation weights (via sigmoid-gated mappings) that adaptively scale the features. Stable responses indicate reliable content, while sharp changes after perturbation highlight degradation-sensitive regions requiring modulation.

2. Prior-informed Uncertainty-guided Reconstruction Module (PURM)

PURM acts as a training-time constraint to enforce physical consistency. It reconstructs the original hazy observation ($\hat{I}$) from the restored image ($\hat{J}$) using the atmospheric scattering model:
$$\hat{I}(x) = \hat{T}(x)\hat{J}(x) + (1 - \hat{T}(x))\hat{A}(x)$$

• Prior Injection: It utilizes Dark Channel Prior (DCP) estimates for transmission ($T_d$) and atmospheric light ($A_d$), injecting them via concatenation and latent affine modulation.
• Uncertainty Coupling: Crucially, PURM inherits the perturbation cues ($N_c, N_s$) generated by the backbone's LPUM (via an inherited I-LPUM block) rather than learning new perturbations. This ensures that regions identified as sensitive during forward dehazing also influence the backward haze reconstruction.
• Loss: A reconstruction loss ($L_{rec}$) minimizes the difference between the reconstructed hazy image and the original input.

3. Dual-space Domain-diversified Distribution-aware Contrastive Loss (D3CL)

D3CL regularizes the feature distributions in both the clean restoration space and the hazy reconstruction space.

• Dual-Space: It applies contrastive learning to both the dehazed output ($\hat{J}$) and the reconstructed hazy image ($\hat{I}$).
• Diversified Negatives: Instead of using only the paired hazy input as a negative, it employs:
  • Real-world negatives: Non-corresponding hazy images from other training pairs to model the broader real-world degradation domain.
  • Synthetic negatives: To cover synthetic haze distributions.
• Stochastic Features: To approximate distribution-aware representations efficiently, perceptual features (extracted via a frozen VGG-19) are perturbed based on their activation magnitude, avoiding expensive Monte Carlo inferences.
• Objective: The loss pulls the anchor toward the positive (clean or original hazy) and pushes it away from real and synthetic negatives in a perturbation-aware perceptual space.

Training vs. Inference: The full framework (LPUM + PURM + D3CL) is used during training. During inference, only the backbone enhanced with the lightweight LPUM is retained; PURM and D3CL are discarded, ensuring minimal additional computational overhead.

Key Contributions

1. BPUL Framework: Introduction of a backbone-agnostic uncertainty learning framework that explicitly models degradation-sensitive feature uncertainty through learnable stochastic perturbations.
2. LPUM: A module that estimates channel-wise and spatial-wise uncertainty responses from perturbation-induced discrepancies, enabling adaptive feature modulation without altering the backbone architecture.
3. PURM: A reconstruction module that imposes a bidirectional physical-consistency constraint by reconstructing the hazy observation from the restored result, guided by transmission/atmospheric priors and shared uncertainty cues.
4. D3CL: A dual-space contrastive loss that regularizes both clean and hazy spaces using real-world and synthetic negatives within a perturbation-aware feature space.
5. Empirical Validation: Extensive experiments demonstrating that BPUL consistently improves multiple representative backbones (MIMOUNet, IRNeXt, HOGformer-S, VIVNet) across five real-world paired benchmarks.

Experimental Results

The authors evaluated BPUL on five real-world paired benchmarks: Dense-Haze, I-HAZE, O-HAZE, NH-HAZE, and LMHaze.

• Performance: BPUL consistently improved all four tested backbones. On average, it improved MIMOUNet by 1.13 dB / 0.031 SSIM, IRNeXt by 0.96 dB / 0.021 SSIM, HOGformer-S by 1.48 dB / 0.061 SSIM, and VIVNet by 1.09 dB / 0.038 SSIM.
• Generality: The method showed robustness across different degradation types (indoor/outdoor, homogeneous/non-homogeneous, varying intensities) and different backbone architectures (CNN, Transformer, hybrid).
• Efficiency: Since PURM and D3CL are training-only constraints, the inference cost is marginal, limited only to the lightweight LPUM operations.
• Ablation Studies:
  • Removing either channel-wise or spatial-wise branches in LPUM degraded performance, confirming the need for joint modeling.
  • Removing learnable perturbation generation reduced PSNR, highlighting the importance of learned distributions.
  • In PURM, removing prior inputs or uncertainty modulation significantly lowered performance, and sharing perturbations between forward and backward modules proved superior to independent estimation.
  • D3CL ablation showed that using non-corresponding real negatives, synthetic negatives, and stochastic VGG features progressively improved results, with the full dual-space formulation yielding the best gains.

Significance and Claims

The paper claims that BPUL provides a general and efficient approach to strengthening real-world dehazing networks. By explicitly learning degradation-sensitive uncertainty and enforcing bidirectional degradation consistency, the framework addresses the ambiguity inherent in real-world haze that deterministic mappings often miss. The authors emphasize that BPUL is backbone-agnostic, meaning it can be integrated into existing state-of-the-art restoration networks with minimal architectural intervention while delivering substantial restoration gains. The approach shifts the paradigm from purely deterministic restoration to uncertainty-aware processing, offering a principled way to handle the physical ambiguities of real-world haze without incurring significant inference overhead.