4KDehazeFlow: UHD Image Dehazing via Continuous Flow

• 4KDehazeFlow is a dehazing method for 4K images that models haze removal as a continuous flow evolution governed by differential equations.
• It integrates a lightweight CNN with a fully learnable 3D lookup table and employs a fourth-order Runge-Kutta solver for precise color correction and efficient dehazing.
• Empirical benchmarks show state-of-the-art performance with high color fidelity, robust structural recovery, and significantly faster inference than diffusion-based approaches.

4KDehazeFlow is a method for ultra-high-definition (UHD) single-image dehazing that frames the restoration process as continuous flow matching via ordinary differential equations, enabling adaptive, high-fidelity removal of haze with computational efficiency and generalizability across network architectures. The core innovation lies in modeling image dehazing as the progressive optimization of a parameterized vector field flow, realized through a combination of a small convolutional neural network (CNN) and a learnable 3D lookup table (LUT), and numerically integrated by a fourth-order Runge-Kutta (RK4) solver. Empirical benchmarks demonstrate state-of-the-art performance, with notable robustness in color fidelity and structural recovery under dense haze conditions (Chen et al., 12 Nov 2025).

1. Formulation of Dehazing as Continuous Flow Matching

4KDehazeFlow recasts the dehazing mapping from hazy input images to clear outputs as a continuous-time flow transformation. Given a hazy image $X_0 = X(t_0)$ and its corresponding clear ground truth $X(t_1)$, the method seeks a vector field $v(X(t), t; \theta)$ that evolves the input via the ODE: $$\frac{dX(t)}{dt} = v(X(t), t; \theta), \qquad X(t_0) = X_0$$ where $\theta$ are learnable parameters. Integrating this equation from $t_0$ to $t_1$ yields the dehazed output $X(t_1)$. The process is thus data-driven, modeling the transformation as a flow from the distribution of hazy images $p_0$ to the clean distribution $p_1$, and is solved in a manner akin to generative models based on continuous normalizing flows.

2. Haze-Aware Vector Field Construction

The time-dependent vector field $v(\cdot)$ is explicitly constructed to combine deterministic atmospheric scattering purification and adaptive color correction: $$v(X_i, t_i) = O_m(X_i) + \lambda O_{\mathrm{lut}}(X_i)$$

• $O_m(X_i)$ is the output of a lightweight encoder-attention-decoder CNN, which, in the style of AOD-Net, estimates a spatially-varying parameter $K(x)$ and bias $b$ for local dehazing. The CNN is defined as:

$$O_m(X_i) = \mathrm{CNN}(X_i) \cdot X_i - \mathrm{CNN}(X_i) + 1$$

and itself structured as $\mathrm{CNN}(X_i) = D(\mathrm{Attn}(E(X_i))) + X_i$, where $E$ and $D$ are the encoder and decoder, respectively, and $\mathrm{Attn}$ denotes spatial attention.

• $O_{\mathrm{lut}}(X_i)$ is the color adjustment generated by trilinear interpolation over a learnable 3D LUT, with contribution scaled by hyperparameter $\lambda$ (optimal value found to be $0.5$). Regularization is provided by using small convolutional kernels (1×1 and 3×3), skip connections, and attention, to balance generalization and artifact suppression.

3. Fully Learnable 3D Lookup Table (Haze-LUT)

The Haze-LUT is a compact, parameter-efficient 3D array with $M^3$ vertices parameterizing the RGB color correction for haze: $$x' = \frac{r^I}{s}, \quad y' = \frac{g^I}{s}, \quad z' = \frac{b^I}{s}$$ where $s = \frac{C_{\max}}{M-1}$, mapping each input pixel $(r^I, g^I, b^I)$ to normalized lattice coordinates. The correction for each pixel is obtained by trilinear interpolation among its eight nearest neighbors, and the LUT itself is trained end-to-end—initialized near the identity for stability, then optimized together with the CNN parameters. This mechanism supports efficient, spatially consistent color transformation during inference.

4. Numerical Flow Integration via Runge-Kutta Method

To solve the continuous ODE defining the transformation, 4KDehazeFlow employs the fourth-order Runge-Kutta (RK4) algorithm: $$\begin{aligned} k_1 &= v(X_i, t_i) \ k_2 &= v\left(X_i + \frac{\Delta t}{2}k_1, t_i + \frac{\Delta t}{2}\right) \ k_3 &= v\left(X_i + \frac{\Delta t}{2}k_2, t_i + \frac{\Delta t}{2}\right) \ k_4 &= v\left(X_i + \Delta t\,k_3, t_i + \Delta t\right) \ X_{i+1} &= X_i + \frac{\Delta t}{6}(k_1 + 2k_2 + 2k_3 + k_4) \end{aligned}$$ with $N$ integration steps of uniform size $\Delta t = (t_1-t_0)/N$ between input and output. Empirical results show RK4 achieves a balance of integration stability and color fidelity, outperforming lower-order (Euler, midpoint) schemes which produce noticeable artifacts.

5. Network Compatibility, Training, and Losses

A salient property of 4KDehazeFlow is its architectural modularity: the haze-aware vector field can encapsulate any backbone dehazing network, not being tied to the specific low-level network implementation. In the canonical formulation, it wraps a small AOD-Net style CNN plus the Haze-LUT; other modern CNNs or transformer architectures can also serve as the “purifier” component, inheriting the flow-matching and integration logic.

Training employs a standard $L_1$ reconstruction loss in RGB space: $\mathcal{L} = \|Y_{\mathrm{gt}} - X_N\|_1$ where $X_N$ is the dehazed image output. Optimization uses AdamW with weight decay $10^{-4}$, batch sizes of 4–8, and learning rates and schedulers set according to the dataset (e.g., $10^{-3}$ for 4KID/SOTS, $10^{-4}$ for I-HAZE/O-HAZE). The ReduceLROnPlateau scheduler with factor 0.5 is applied after plateaus of 100 epochs.

6. Empirical Results and Qualitative Analysis

4KDehazeFlow demonstrates superior quantitative performance on several benchmarks. Notable results include:

Dataset	PSNR (dB)	Δ PSNR	SSIM	Δ SSIM	LPIPS	NIQE
4KID	23.85	+0.11	—	—	0.1101	—
I-HAZE	19.63	+0.83	0.8085	+0.04	—	—
O-HAZE	—	—	0.8138	+0.11	—	—
Average	21.62	+2.08	0.8534	—	0.3124	—
SOTS	—	—	0.9709	—	0.0478	3.47

A key empirical finding is that under challenging dense haze conditions and 4K real-world imagery, 4KDehazeFlow reconstructs image structures with reduced artifacts and superior color fidelity compared to both prior-based and diffusion-based approaches, while delivering inference two to three orders of magnitude faster than diffusion sampling.

7. Complete Pipeline and Implementation Outline

The core inference loop is governed by the following algorithm:

X = X0 for i in range(N): t = t0 + i * dt k1 = v(X, t, θ) k2 = v(X + 0.5 * dt * k1, t + 0.5 * dt, θ) k3 = v(X + 0.5 * dt * k2, t + 0.5 * dt, θ) k4 = v(X + dt * k3, t + dt, θ) X = X + (dt / 6) * (k1 + 2 * k2 + 2 * k3 + k4) X_N = X # Output: dehazed image

Each call to $v(\cdot)$ computes the haze-aware purification and LUT color correction for the current image state. This end-to-end ODE-based solver, when paired with lightweight CNN design and compact LUT, enables both scalability to 4K resolutions and flexibility in network choice. Ablation indicates the modular design and numerical integrator are essential to artifact suppression and cross-domain performance. The approach represents an overview of contemporary continuous flow-matching techniques with application-specific priors tailored for image dehazing at UHD scales (Chen et al., 12 Nov 2025).