RTE-FM-Dehazer: Radiative Transfer Equation Inspired Flow Matching for Real-World Image Dehazing¶

🕒 Published (v1): 2026-07-02 06:06 UTC · Source: Arxiv · link

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TL;DR¶

RTE-FM-Dehazer reformulates single-image dehazing as physics-regularized flow matching in the latent space of Stable Diffusion, using the diffusion-absorption term of the Radiative Transfer Equation (RTE) as a soft prior to steer the generative trajectory. To overcome the scarcity of real hazy/clear pairs, the authors use VLMs (Qwen2.5-VL, Gemini) to synthesize a 50k-pair dataset (P-HAZE) with geometry-aware pixel alignment. The method achieves state-of-the-art PSNR and LPIPS on five real-world dehazing benchmarks while generalizing across diverse haze types.

Problem¶

The dominant Atmospheric Scattering Model (ASM) assumes single scattering and homogeneous media — assumptions routinely violated in real haze — causing residual haze and color drift. Diffusion- and VQGAN-based generative methods address realism but introduce stochastic color drift and patch artifacts because they are unconstrained by any physical haze-formation model. Additionally, real-world paired hazy/clear training data is scarce, and ASM-based synthesis is too simplistic to reproduce natural haze complexity.

Method¶

The method operates in the latent space of a frozen SD 2.1 VAE encoder (\(64\times64\times4\) latent). A U-Net learns a velocity field \(\boldsymbol{v}_\theta\) via flow matching, which minimizes the distance to the optimal-transport direction \((\mathbf{z}_1 - \mathbf{z}_0)\). The key addition is a physics-inspired RTE regularizer derived from the diffusion approximation of the full RTE:

\[\frac{\partial u}{\partial t} = D\nabla^2 u - \mu_a u\]

The RTE velocity in latent space is defined (with sign-flipped for haze removal) as:

\[\mathbf{v}_{\text{RTE}}(\mathbf{z}) \triangleq -D\nabla^2\mathbf{z} + \mu_a\mathbf{z}\]

The Laplacian is discretized via a five-point stencil convolution kernel. \(D\) is estimated by a \(1\times1\) conv + softplus; \(\mu_a = \kappa\langle|\mathbf{z}_t|\rangle\) with \(\kappa=0.1\). The combined training loss is:

\[\mathcal{L} = \|\boldsymbol{v}_\theta - (\mathbf{z}_1 - \mathbf{z}_0)\|^2 + \lambda\|\boldsymbol{v}_\theta - \mathbf{v}_{\text{RTE}}\|^2\]

with \(\lambda=0.5\). At inference, the ODE is solved via multi-step Euler integration (≥10 steps recommended).

For data, VLMs generate hazy images from stochastic text prompts applied to clean reference images. Alignment is achieved by estimating a homography \(\mathbf{H}\in\mathbb{R}^{3\times3}\) from 800–1500 dense keypoint matches, then bilinear-warping the hazy frame. SAM2 segmentation verification and human inspection filter semantic artifacts.

Key Contributions¶

Physics-regularized flow matching: RTE diffusion-absorption term embedded as an L2 regularizer on the learned velocity field, steering the dehazing trajectory without restricting it to ASM assumptions.
Deterministic latent trajectory: replacing stochastic diffusion noise priors with the RTE regularizer preserves global color distribution better than random-sampling baselines.
P-HAZE dataset: 50,000 rigorously aligned hazy/clear pairs synthesized via VLM prompting (Qwen2.5-VL / Gemini) + homography warping, covering diverse scenes, seasons, and camera sensors.

Results¶

NH-HAZE: 19.53 dB PSNR, 0.600 SSIM, 0.233 LPIPS — outperforms the next best (LHTD: 15.60 dB) by +3.9 dB PSNR and −37% LPIPS.
SMOKE: 18.67 dB PSNR, 0.554 SSIM, 0.222 LPIPS — +3.0 dB over LHTD (15.67 dB) and −37% LPIPS.
I-HAZE: 18.81 dB PSNR, 0.812 SSIM, 0.145 LPIPS (best PSNR; second-best SSIM/LPIPS behind DehazeFormer/DEANet on SSIM).
P-HAZE: 20.29 dB PSNR, 0.792 SSIM, 0.159 LPIPS (best across all metrics on this test split).
RESIDE-6K: 21.77 PSNR, 0.858 SSIM, 0.068 LPIPS (best PSNR; DehazeFormer/DEANet achieve higher SSIM of 0.981/0.980 on this synthetic set).
Achieves highest PSNR on 4/6 benchmarks and lowest LPIPS on 5/6 benchmarks.
Trained only on P-HAZE; zero real paired data used.

Limitations¶

RTE approximation in latent space is a structural analogy rather than a rigorous physical derivation; the pretrained VAE decoder acting as "local isometry" is an approximation that may not hold far from the training manifold.
On the synthetic RESIDE-6K benchmark, methods trained on in-domain synthetic data (DehazeFormer SSIM 0.981, DEANet SSIM 0.980) outperform the proposed method (SSIM 0.858), indicating a remaining gap for spatially homogeneous synthetic haze.
Inference requires ≥10 Euler steps for high quality, which is more expensive than single-step methods.
P-HAZE generation relies on VLM image-editing quality and a human-in-the-loop filtering step, limiting full automation and scalability.
\(\mu_a\) absorption coefficient \(\kappa=0.1\) is set empirically; the sensitivity range [0.3, 0.7] for \(\lambda\) is narrow enough that out-of-range settings are untested.

Relevance to Vision-Language Models¶

VLMs (Qwen2.5-VL and Gemini) play a central role in this work as image-editing engines for scalable paired data synthesis: given a clean image and a stochastic haze prompt, the VLM generates a realistic hazy counterpart that implicitly respects scene geometry and spatial depth without requiring handcrafted depth maps or weather parameters. This demonstrates a practical pattern — leveraging VLM image-understanding and editing capabilities to bootstrap training data for low-level vision tasks where real paired supervision is impractical. For researchers tracking VLMs, this paper is a concrete case study of VLMs as data-generation infrastructure rather than as inference-time reasoning models, complementing emerging work on VLM-driven dataset construction pipelines.