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

Conference: ECCV 2026
Paper: ECCV Official Link
Code: https://github.com/vincentweikey/RTE-FM-Dehazer
Area: Image Restoration / Image Generation
Keywords: Image Dehazing / Flow Matching / Radiative Transfer Equation / Physics-inspired Regularization / VLM Data Synthesis

TL;DR

Addressing the failure of atmospheric scattering models in non-homogeneous real haze and the color drift in generative dehazing, RTE-FM-Dehazer embeds reduced Radiative Transfer Equation (RTE) diffusion-absorption dynamics as a tangent-space regularizer into continuous flow matching, paired with a 50k VLM-synthesized, geometrically aligned dataset (P-HAZE) to achieve artifact-free, high-fidelity real-world dehazing.

Background & Motivation

Single-image dehazing has long relied on the classical Atmospheric Scattering Model (ASM) as a core physical prior to invert hazy observations into clean scene radiance. However, the ASM is founded on restrictive assumptions of single scattering and homogeneous participating media. In natural outdoor haze, dense fog, or fire smoke, suspended aerosols exhibit pronounced anisotropic multiple scattering and non-uniform density distributions across scene depths. Hand-crafted heuristics (such as the Dark Channel Prior, Color-Line, and Haze-Line priors) as well as modern CNN and Transformer architectures (e.g., FFA-Net, DEA-Net) trained on homogeneous synthetic pairs routinely suffer from prior breakdown in real-world scenarios, leading to severe residual haze, over-saturation, and chromatic distortions.

To mitigate dependency on idealized synthetic data, recent research turned to generative restoration models based on diffusion processes (e.g., DehazeDiff) or discrete VQ-GAN codebook priors (e.g., RIDCP, IPC-Dehaze). Although these generative formulations improve perceptual sharpness, their unconstrained nature introduces severe structural artifacts: the stochastic reverse sampling of diffusion models frequently triggers color shifts across adjacent spectral bands, whereas discrete codebook retrieval occasionally splices extraneous visual patterns not present in the original field of view. Furthermore, because collecting large-scale, pixel-aligned real-world hazy/clean image pairs is practically infeasible, existing approaches remain trapped between oversimplified physical models and unconstrained, hallucination-prone generative priors.

This paper identifies that real-world media transport is accurately governed by the Radiative Transfer Equation (RTE), which naturally accounts for both absorption and multiple scattering. Crucially, the diffusion-absorption approximation of the RTE shares an identical differential structure with the instantaneous velocity field in continuous flow matching. Core idea: regularize the deterministic latent velocity field of flow matching via tangent-space projection onto a reduced Radiative Transfer Equation (RTE) diffusion-absorption operator, coupled with a scalable VLM-driven and homography-aligned data synthesis pipeline (P-HAZE) to achieve physically grounded, artifact-free real-world dehazing.

Method

Overall Architecture

RTE-FM-Dehazer formulates single-image dehazing as an optimal transport flow matching process within the latent manifold of a pre-trained Stable Diffusion VAE. As illustrated below, at the macro level, a frozen VAE encoder maps a hazy input \(x_{\text{hazy}}\) into an initial latent state \(z_0 \in \mathbb{R}^{4\times 64\times 64}\), targeting the clean latent representation \(z_1\). At the micro level, along the continuous trajectory \(t \in [0, 1]\), a U-Net neural velocity field is simultaneously supervised by the straight-line displacement vector and a local diffusion-absorption velocity field derived from the RTE.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Hazy & Clean Image Inputs"] --> B["VLM Haze Generation & Homography Alignment<br/>Scalable P-HAZE Dataset Construction"]
    B --> C["Frozen VAE Latent Encoding<br/>Obtain Hazy Latent z_0 and Clean Latent z_1"]
    C --> D["Linear Trajectory Interpolation z_t & Latent Features"]
    D --> E["RTE Diffusion-Absorption Physics Regularizer<br/>Five-point Stencil Laplacian & Adaptive Absorption"]
    D --> F["U-Net Latent Velocity Field Prediction v_θ"]
    E & F --> G["Joint Tangent-Space Velocity L2 Projection Loss<br/>L_FM Transport Fit + λ L_RTE Physical Consistency"]
    G --> H["Deterministic Multi-Step Euler ODE Integration<br/>dz/dt = v_θ(z,t) from z_0 to Recovered z_1"]
    H --> I["VAE Decoder Rendering Haze-Free Image"]

Key Designs

1. Radiative Transfer Equation Inspired Diffusion-Absorption Regularizer: Constraining Tangent-Space Energy Flux While the full integro-differential RTE is computationally intractable for end-to-end inversion, its diffusion approximation cleanly captures the macroscopic energy transport in participating media: $$ \frac{\partial u}{\partial t} = D \nabla^2 u - \mu_a u $$ Here, the spatial diffusion term \(D \nabla^2 u\) governs the redistribution of radiative energy across spatial gradients, naturally smoothing out sharp boundary discontinuities and halo artifacts. The absorption term \(-\mu_a u\) models exponential radiative energy decay through the medium, directly driving the state toward the haze-free manifold. The authors bridge physical radiance to the latent feature space \(z \in \mathbb{R}^{4\times 64\times 64}\), discretizing the spatial Laplacian via a 5-point stencil convolution kernel \(K_{\nabla^2}\). The diffusion coefficient \(D\) is predicted adaptively through a \(1\times 1\) convolution with Softplus activation, and absorption strength is quantified without decoding by \(\mu_a = \kappa \langle |z_t| \rangle\) with \(\kappa = 0.1\). Reversing the sign to orient energy decay toward clarity yields the target physical velocity: $$ v_{\text{RTE}}(z) = -D \nabla^2 z + \mu_a z $$

2. Deterministic Latent Flow Matching with L2 Projection: Eliminating Stochastic Sampling and Color Casts Unlike diffusion models that rely on stochastic reverse Wiener paths, flow matching operates on a deterministic vector field along linear probability paths \(z_t = (1-t)z_0 + t z_1\). To enforce optical plausibility at every point along the integration trajectory, the training objective unites optimal transport regression with physical flux consistency: $$ \mathcal{L} = \underbrace{|v_\theta(z_t, t) - (z_1 - z_0)|^2}{\text{Transport Fit}} + \lambda \underbrace{|v\theta(z_t, t) - v_{\text{RTE}}(z_t)|^2_{\text{F}}}_{\text{RTE Physical Fit}} $$ Minimizing this combined loss performs an \(L_2\) projection of the data-driven velocity onto the tangent space of the RTE operator. At test time, dehazing is executed via explicit Euler integration \(\frac{\mathrm{d}z}{\mathrm{d}t} = v_\theta(z, t)\) using \(T > 10\) steps. Because \(v_\theta\) outputs spatially varying full-resolution vectors, dense fog, highlights, and shadow regions evolve at localized, physically compliant speeds without random color drift.

3. VLM-Driven Scalable Generation and Sub-Pixel Homography Alignment: Solving Real Data Scarcity To bypass the lack of real paired data without succumbing to synthetic ASM artifacts, the authors design an automated synthesis pipeline utilizing state-of-the-art vision-language models (Qwen2.5-VL and Gemini-2-Flash). Natural clean reference images from high-resolution outdoor datasets (DIV2K, Flickr2K, Unsplash2K, Mapillary Vistas) are perturbed via stochastic text prompts specifying realistic, non-stationary smoke and depth-varying fog plumes. To correct slight camera-intrinsic and optical distortion offsets introduced by VLM edits, dense keypoint correspondences (800–1,500 inliers) are matched to estimate a planar homography \(H \in \mathbb{R}^{3\times 3}\), warping the hazy frame into sub-pixel alignment: $$ I_{\text{aligned}}(x) = I_{\text{hazy}}(H^{-1}x) $$ Semantic integrity is verified via SAM2 segmentation consistency checks and human audit, curating the 50,000-pair P-HAZE dataset.

Loss & Training

The framework builds on the Stable Diffusion 2.1 VAE (\(8\times\) spatial downsampling). The velocity U-Net incorporates 4-level encoder-decoder blocks with spatial self-attention at the bottleneck. Training is conducted with nominal weight \(\lambda = 0.5\) (exhibiting stable convergence across \([0.3, 0.7]\)). The model is optimized using Adam with an initial learning rate of \(1\times 10^{-4}\) (halved every 50 epochs) and a batch size of 64, training for 200 epochs on a single NVIDIA RTX 4090 GPU in approximately 20 hours.

Key Experimental Results

Main Results

Trained exclusively on the synthetic P-HAZE dataset, RTE-FM-Dehazer is evaluated across six diverse benchmarks without fine-tuning: I-HAZE (indoor fog chamber), D-HAZE (dense glycol suburban fog), NH-HAZE (real outdoor non-homogeneous haze), SMOKE (real combustion plumes), P-HAZE test set, and RESIDE-6K (synthetic baseline). Evaluation metrics include PSNR, SSIM, and deep perceptual similarity LPIPS.

Main quantitative comparison from Table 1 of the original paper:

Dataset	Metric	Ours (RTE-FM)	Prev. SOTA (Runner-up)	Gain / Distinction
NH-HAZE (Real non-homogeneous)	PSNR ↑ SSIM ↑ LPIPS ↓	19.53 0.600 0.233	15.60 (LHTD) 0.644 (IPC-Dehaze) 0.371 (LHTD)	+3.93 dB -0.044 -37.2% LPIPS
SMOKE (Real fire smoke)	PSNR ↑ SSIM ↑ LPIPS ↓	18.67 0.554 0.222	15.67 (LHTD) 0.588 (IPC-Dehaze) 0.336 (IPC-Dehaze)	+3.00 dB -0.034 -33.9% LPIPS
I-HAZE (Real indoor fog)	PSNR ↑ SSIM ↑ LPIPS ↓	18.81 0.812 0.145	16.96 (DEANet) 0.817 (RIDCP) 0.179 (RIDCP)	+1.85 dB -0.005 -19.0% LPIPS
D-HAZE (Extreme density fog)	PSNR ↑ SSIM ↑ LPIPS ↓	12.56 0.480 0.528	12.84 (LHTD) 0.474 (RIDCP) 0.580 (LHTD)	-0.28 dB +0.006 -9.0% LPIPS
P-HAZE (VLM-synthesized real)	PSNR ↑ SSIM ↑ LPIPS ↓	20.29 0.792 0.159	18.05 (DEANet) 0.786 (DEANet) 0.233 (IPC-Dehaze)	+2.24 dB +0.006 -31.8% LPIPS
RESIDE-6K (Synthetic baseline)	PSNR ↑ SSIM ↑ LPIPS ↓	21.77 0.858 0.068	31.78 (DEANet) 0.981 (DehazeFormer) 0.012 (DEANet)	-10.01 dB (Overfitted to ASM) -0.123 +0.056

Ablation Study

To rigorously demonstrate the necessity of each RTE component and assess alternative priors, five variants were evaluated under identical training setups.

Ablation study on regularizer components from Table 2 of the original paper:

Config	P-HAZE (PSNR/SSIM/LPIPS)	NH-HAZE (PSNR/SSIM/LPIPS)	SMOKE (PSNR/SSIM/LPIPS)	Note / Analysis
Full model (RTE-FM)	20.29 / 0.792 / 0.159	19.53 / 0.600 / 0.233	18.67 / 0.554 / 0.222	Complete tangent-space projection combining diffusion & absorption
Absorb-only FM	18.11 / 0.636 / 0.378	12.77 / 0.459 / 0.441	11.88 / 0.400 / 0.399	Lacks spatial diffusion smoothing, producing blotchy artifacts (-6.76 dB on NH-HAZE)
Diffusion-only FM	18.91 / 0.552 / 0.356	13.85 / 0.505 / 0.480	12.21 / 0.421 / 0.411	Lacks radiative energy decay drive, leaving heavy haze remnants
DCP-regularizer FM	17.22 / 0.621 / 0.344	12.22 / 0.523 / 0.547	11.19 / 0.398 / 0.412	Heuristic hard constraints conflict with continuous flow paths, degrading below Vanilla FM
Rectified Flow	19.21 / 0.768 / 0.254	12.99 / 0.494 / 0.491	13.40 / 0.463 / 0.372	Purely data-driven straight lines fail to generalize across non-homogeneous real haze
Vanilla FM	20.12 / 0.785 / 0.159	13.78 / 0.507 / 0.406	13.77 / 0.488 / 0.351	Drastic out-of-domain degradation (falls 5.75 dB behind RTE-FM on NH-HAZE)

Key Findings

• Physical inductive bias governs out-of-domain generalization: Methods tuned on synthetic ASM benchmarks (e.g., DEANet achieving 31.78 dB on RESIDE-6K) experience catastrophic collapse on non-homogeneous real haze (12.38 dB on NH-HAZE). In contrast, RTE-FM-Dehazer maintains 19.53 dB on NH-HAZE, proving that incorporating multi-scattering physics is essential for real-world robustness.
• Mutual necessity of diffusion and absorption: Ablation data confirms that stripping either term causes catastrophic drops (>5.5 dB on NH-HAZE). Spatial diffusion suppresses spatial discontinuities, while absorption drives the energy flow monotonically toward the clear manifold.
• Incompatibility of handcrafted priors with flow matching: Explicitly penalizing dark-channel prior gradients within flow matching severely impairs performance (12.22 dB vs. 13.78 dB of unconstrained Vanilla FM), demonstrating that heuristic low-order statistics disrupt the optimal transport geometry.

Highlights & Insights

• Tangent-space integration of physics PDE into generative ODEs: Rather than solving the forward physics model explicitly or predicting scalar physical maps, the paper maps the instantaneous rate of change of the RTE into the velocity tangent space of continuous flow matching, establishing a mathematically sound bridge between physical transport and generative modeling.
• Deterministic flow suppresses generative hallucination: By transitioning from stochastic diffusion sampling to deterministic ODE integration, the model eliminates random trajectory drift, strictly preserving input illumination structures and authentic local colors.
• Scalable VLM + homography pipeline: Demonstrates a practical methodology to generate 50k physically plausible, non-homogeneous haze training pairs from web-scale clean images via VLMs, utilizing sub-pixel geometric homography and SAM2 filtering to bypass physical capture constraints.

Limitations & Future Work

• High-frequency detail attenuation in latent space: Relying on an \(8\times\) downsampling VAE encoder incurs minor texture loss in scenes with microscopic typography or severe occlusion; exploring direct pixel-space flow matching remains an important future avenue.
• Planar homography approximation limits: Sub-pixel alignment relies on a single \(3\times 3\) planar homography matrix, which may exhibit minor local misalignments in scenes featuring dramatic parallax and non-planar multi-depth geometries.
• Multi-step ODE numerical solver overhead: High perceptual fidelity requires \(T > 10\) Euler integration steps during inference; incorporating consistency distillation or adaptive step solvers will be necessary for real-time mobile and edge deployment.

Related Work & Insights

• vs. DCP & Hand-crafted ASM Priors: Classical methods assume homogeneous optical thickness and single scattering, causing extensive color cast and halo artifacts; RTE-FM-Dehazer accommodates non-homogeneous media and multiple scattering through continuous PDE regularization.
• vs. Diffusion Dehazers (e.g., DehazeDiff): Diffusion restoration relies on stochastic reverse trajectories that are sensitive to noise scheduling and prone to color drift; RTE-FM-Dehazer enforces a deterministic ODE path aligned with physical energy decay.
• vs. VQ-GAN Priors (e.g., RIDCP, IPC-Dehaze): Discrete codebook indexing frequently retrieves out-of-view visual tokens, causing boundary splicing artifacts; RTE-FM-Dehazer performs continuous transport in latent space, avoiding discrete clustering errors.

Rating

• Novelty: ⭐⭐⭐⭐⭐ (Elegant unification of radiative transfer equation dynamics with the tangent velocity field of flow matching)
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ (Extensive validation across six diverse real and synthetic benchmarks with comprehensive physical ablations)
• Writing Quality: ⭐⭐⭐⭐⭐ (Clear mathematical formulation, tight conceptual integration, and clean narrative structure)
• Value: ⭐⭐⭐⭐⭐ (Provides an impactful paradigm for incorporating physical PDE constraints into continuous-time generative restoration models)

Related Papers

• [ECCV 2026] Physics Meets Perception: A Reinforcement Learning Framework for Unpaired Real-World Image Dehazing
• [ICCV 2025] Contrastive Flow Matching (ΔFM)
• [ECCV 2026] AdaBridge-SR: Adaptive Bridge Matching for Real-World Image Super-Resolution
• [ECCV 2026] Entropy-Controlled Flow Matching
• [AAAI 2026] Continuous Degradation Modeling via Latent Flow Matching for Real-World Super-Resolution