💻 computer science

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

The paper introduces RTE-FM-Dehazer, a novel dehazing framework that leverages the Radiative Transfer Equation to guide a flow matching model and utilizes a large-scale synthetic dataset (P-HAZE) generated by vision-language models to overcome the limitations of traditional atmospheric scattering assumptions and achieve superior performance on real-world hazy images.

Original authors: Chenfeng Wei, Chun Wang, Boyang Zhao, Si Zuo, Shenhong Wang, Chenguang Yang

Published 2026-07-03

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CC BY 4.0

Original authors: Chenfeng Wei, Chun Wang, Boyang Zhao, Si Zuo, Shenhong Wang, Chenguang Yang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to look through a dirty, foggy window to see a beautiful garden outside. The glass is covered in a thick, uneven layer of smog and dust. Your goal is to "clean" the view so you can see the flowers and trees clearly again. This is what image dehazing does for computers: it tries to take a blurry, gray photo and turn it back into a sharp, colorful one.

For a long time, computers tried to solve this by using a simple, old rulebook called the "Atmospheric Scattering Model." Think of this rulebook like a child's guess: "If the picture is gray, just add some color back." The problem is that real-world fog is messy. It's not just a uniform gray blanket; it swirls, it gets thicker in some spots, and it absorbs light differently depending on what it's hitting. The old rulebook couldn't handle this complexity, often leaving behind a "ghost" of the fog or making the colors look weird (like turning a green tree blue).

Enter RTE-FM-Dehazer.

The authors of this paper built a new, smarter way to clean up these photos. They combined three main ideas, which we can explain with some everyday analogies:

1. The Better Rulebook: The "Physics of Fog" (RTE)

Instead of using the simple child's guess, the team used a much more complex and accurate physics equation called the Radiative Transfer Equation (RTE).

The Analogy: Imagine the old method was like trying to clean a window by just wiping it with a dry cloth. The new method is like understanding exactly how the dirt is stuck to the glass, how it absorbs light, and how it scatters. It accounts for the fact that fog isn't just a flat layer; it's a 3D cloud that eats up light and bounces it around. By using this "physics of fog," the computer knows exactly how to reverse the mess without accidentally painting over the flowers or making the sky look purple.

2. The Guided Path: "Flow Matching"

The computer doesn't just guess the answer in one big leap. Instead, it uses a technique called Flow Matching.

The Analogy: Imagine you are lost in a thick fog and need to get home.
- Old methods might try to teleport you home instantly, but they often teleport you into a wall or a swamp because they don't know the terrain.
- RTE-FM-Dehazer acts like a GPS that guides you step-by-step. It breaks the journey into tiny, invisible steps. At every single step, it asks, "If I move a tiny bit, does this look more like a clear day?"
- Crucially, it uses the "Physics of Fog" (from point #1) as a compass. It ensures that every tiny step you take follows the natural laws of how light travels. This stops the computer from wandering off into "weird color land" and keeps the picture looking natural.

3. The Infinite Training Class: "The AI Artist" (P-HAZE)

To learn how to do this, the computer needs to practice on thousands of examples of "foggy photos" and their matching "clear photos." But in the real world, it's almost impossible to find a clear photo and a foggy photo of the exact same scene taken at the exact same moment.

The Analogy: The authors realized they couldn't wait for nature to provide enough practice tests. So, they built a virtual training factory.
- They used a super-smart AI (a Vision-Language Model) that acts like a digital artist. You give the artist a clear photo and say, "Draw thick, swirling smoke over this, but keep the trees and cars exactly where they are."
- The artist creates a realistic foggy version. Then, the computer uses a "digital ruler" to make sure the foggy version lines up perfectly with the original clear version.
- They did this 50,000 times, creating a massive library called P-HAZE. This gave the computer endless practice without needing real-world foggy days.

The Result

When they tested this new system, it worked like magic compared to the old ways:

No Ghosts: It removed the fog completely without leaving behind gray "ghosts" or blurry spots.
True Colors: It didn't accidentally turn a sunny day into a sunset or a green forest into a purple swamp.
Real-World Ready: It worked great on photos of smoke, heavy fog, and uneven haze, even on pictures it had never seen before.

In short: The paper presents a new tool that cleans up foggy photos by using a deep understanding of how light and fog actually interact (Physics), guiding the cleanup process step-by-step like a GPS (Flow Matching), and training on a massive, AI-generated library of practice photos (P-HAZE). The result is a clear, natural-looking image that respects the original scene's colors and details.

Technical Summary: RTE-FM-Dehazer

Problem Statement

Single-image dehazing aims to recover a clear scene from a hazy observation but remains an ill-posed problem. Existing approaches face two primary limitations:

Reliance on Simplified Physical Priors: Prevailing methods utilize the Atmospheric Scattering Model (ASM). The ASM assumes single scattering and homogeneous media, assumptions frequently violated in real-world scenarios where haze is spatially non-uniform and light undergoes multiple scattering. This leads to residual haze, color drift, and over-enhanced artifacts.
Data Scarcity and Synthesis Limitations: Large-scale, real-world paired hazy/clear datasets are impractical to collect. Existing synthesis methods often rely on the same restrictive ASM assumptions, failing to reproduce the full complexity of natural haze (e.g., anisotropic scattering, depth-dependent attenuation). Furthermore, recent generative approaches (Diffusion, VQGAN) introduce stochastic artifacts, such as color drift or patch grafting, due to their lack of physical constraints.

Methodology: RTE-FM-Dehazer

The authors propose RTE-FM-Dehazer, a framework that reformulates dehazing as a physics-inspired Flow Matching task regularized by the Radiative Transfer Equation (RTE).

1. Physics-Inspired Regularization (RTE vs. ASM)

Instead of the ASM, the method employs the RTE, which jointly accounts for scattering and absorption, naturally accommodating non-homogeneous and multiple-scattering media.

Flow Matching Formulation: The dehazing process is modeled as a continuous trajectory from a hazy latent state ( $z_0$ ) to a clean latent state ( $z_1$ ). A neural network ( $v_\theta$ ) predicts a velocity field to evolve the image via an Ordinary Differential Equation (ODE).
RTE-Derived Regularizer: The authors draw a structural similarity between the RTE diffusion-absorption term and the ODE in flow matching. They derive a velocity term from a reduced RTE:
$\mathbf{v}_{\text{RTE}}(\mathbf{z}) \triangleq -D\nabla^2\mathbf{z} + \mu_a\mathbf{z}$
Here, $-D\nabla^2\mathbf{z}$ models spatial diffusion (smoothing gradients), and $\mu_a\mathbf{z}$ models medium absorption (exponential decay of radiance).
Combined Loss: The network is trained to minimize a combined loss function that aligns the predicted velocity with both the optimal transport direction ( $z_1 - z_0$ ) and the RTE-derived velocity:
$\mathcal{L} = \|\mathbf{v}_{\theta} - (\mathbf{z}_1 - \mathbf{z}_0)\|^2 + \lambda \|\mathbf{v}_{\theta} - \mathbf{v}_{\text{RTE}}\|^2$
This ensures the generated trajectory is physically plausible (satisfying RTE dynamics) while remaining data-driven.

2. Scalable Data Pipeline (P-HAZE)

To address the lack of real paired data, the authors introduce a pipeline to generate a large-scale dataset, P-HAZE (50,000 pairs):

VLM-Driven Generation: Leveraging Vision-Language Models (e.g., Qwen2.5-VL, Gemini-2-Flash), the system generates realistic hazy images from clean references using text prompts. This captures complex, non-stationary aerosol distributions (e.g., swirling smoke) without handcrafted depth maps.
Geometric Alignment: Since VLM outputs may have slight geometric distortions, the pipeline extracts dense keypoints and estimates a planar homography to warp the hazy image into pixel-wise alignment with the clean reference.
Filtering: A two-stage filtering strategy (SAM2 segmentation + human-in-the-loop) removes semantic artifacts.

3. Architecture and Training

Latent Space: The model operates in the latent space of Stable Diffusion v2.1 (64x64x4) to reduce computational cost while preserving texture.
Network: A U-Net backbone predicts the velocity field.
Inference: The clean image is recovered by solving the ODE via multi-step Euler integration (recommended >10 steps) to simulate the gradual transition from hazy to clean.

Key Contributions

RTE-Regularized Flow Matching: The authors reformulate single-image dehazing by integrating the Radiative Transfer Equation as a soft prior into the flow matching framework. This replaces the restrictive ASM, aligning the generative trajectory with physical light transport dynamics for more stable and realistic results.
Deterministic Generation: By removing stochastic noise priors and regularizing the flow with a diffusion-absorption term, the method yields a deterministic latent trajectory that better preserves the original color distribution compared to random-sampling baselines.
P-HAZE Dataset: A scalable, VLM-driven pipeline is proposed to synthesize 50,000 realistic hazy/clear pairs, enabling robust training without reliance on scarce real-world data.

Experimental Results

The model was trained solely on the synthetic P-HAZE dataset and evaluated on five diverse real-world benchmarks (I-HAZE, D-HAZE, SMOKE, NH-HAZE, RESIDE-6K).

Quantitative Performance: RTE-FM-Dehazer achieved the highest PSNR on four datasets and the lowest LPIPS on five out of six benchmarks. Notably, on the challenging NH-HAZE dataset, it outperformed the strongest competitor (LHTD) by +3.9 dB in PSNR and reduced LPIPS by 37%.
Generalization: Unlike supervised methods that degrade on real-world data due to domain shift, RTE-FM-Dehazer demonstrated strong cross-domain generalization, maintaining performance across indoor, outdoor, and smoke-laden scenes.
Qualitative Analysis: Visual comparisons show the method effectively removes spatially varying haze and color casts while preserving fine textures and original lighting structures. It avoids the residual haze of CNN/Transformer methods and the color drift/artifacts of generative (GAN/Diffusion) baselines.
Ablation Studies: Removing the RTE regularizer (Vanilla FM) or decoupling its components (Absorb-only or Diffusion-only) led to significant performance drops, confirming that the integrated absorption-diffusion formulation is critical for handling non-uniform haze.

Significance and Claims

The paper claims that RTE-FM-Dehazer addresses the core limitations of current dehazing methods by bridging the gap between data-driven generative models and physical laws. By embedding the RTE directly into the flow matching velocity field, the method achieves a "physically regularised transport equation" that produces sharper, color-consistent, and artifact-free results. The authors assert that this approach offers a robust solution for real-world dehazing without requiring paired real-world training data, leveraging the structural similarity between radiative transfer and flow matching to guide the generative process.

Future work, as noted by the authors, involves moving from latent space to pixel space to eliminate VAE information loss and investigating efficient numerical solvers for full-resolution processing.