LearnIR: Posterior Sampling for Image Restoration – Face Shadow Removal & Dehazing (ICLR 2026)

Problem Background

Real‑world imaging often suffers from multiple heterogeneous degradations (e.g., haze, shadows, noise, motion blur) that occur simultaneously, making image restoration a severely ill‑posed inverse problem.

Existing diffusion‑based restoration methods face three core limitations:

Conditional generation: difficulty balancing faithful restoration with realistic generation.

Inversion‑based approaches: error accumulation during mapping degraded images to latent space and low efficiency.

Posterior‑sampling methods (e.g., DPS): require an exact forward degradation operator A, which is unavailable in practice.

Core Contributions

Learnable diffusion posterior sampling framework (LearnIR): a lightweight network directly predicts the gradient‑correction distribution, eliminating the need for a known forward operator and overcoming the key restriction of traditional DPS.

Diffusion posterior sampling correction (DPSC): leveraging the closure property of Gaussian distributions, the authors prove that the bias between the true posterior and the model‑predicted reverse distribution follows a Gaussian. A lightweight network μ_θ is trained to fit the analytic mean μ, providing an plug‑and‑play regularization term that aligns the sampling trajectory with the true posterior, removing structural bias and color shift.

Dynamic resolution module (DRM): a time‑dependent resolution‑scheduling strategy implements a coarse‑to‑fine sampling process: low‑noise stages use low resolution to capture global context, while high‑noise stages recover high‑resolution fine textures. This is achieved with non‑trainable bilinear interpolation, avoiding a pretrained VAE and reducing computational cost.

Key Theory

Theorem 1 shows that in the DRM latent space, the DPS gradient is proportional to the bias between the model‑predicted reverse distribution and the true forward‑posterior distribution. Both the mean μ and variance σ² have closed‑form solutions; training μ_θ to approximate μ effectively guides the sampling trajectory toward the true posterior.

Method Details

DPSC loss: combines a denoising loss that forces the noise‑prediction network ε_θ to estimate residual noise, with a consistency loss that forces μ_θ to fit the analytic mean of the forward‑reverse posterior bias. The total loss is λ·(denoising + consistency). During inference, DPSC predicts gradient corrections at each sampling step, adaptively correcting the diffusion path.

Training and Inference

The training follows a two‑stage strategy:

Stage 1: train DPSC with DRM disabled (fixed resolution) to focus on learning gradient corrections.

Stage 2: enable DRM and fine‑tune with a smaller learning rate under dynamic resolution.

Inference determines a stable sampling start point T′ via a residual‑diffusion smooth equivalence transform, requiring only 5 sampling steps to generate high‑quality results.

Experimental Results

Evaluations were conducted on five datasets: ISTD (shadow removal), O‑HAZE, HazyDet, REVIDE (dehazing), and a newly built FaceShadow dataset (face shadow removal, 30 k synthetic pairs + 1 k real pairs). All experiments ran on a single A100 GPU with 5‑step sampling.

Shadow removal (ISTD): LearnIR achieved the best performance among mask‑based methods and remained competitive with the top mask‑free approaches.

Dehazing (O‑HAZE / HazyDet / REVIDE): LearnIR outperformed all baselines, improving PSNR by +2.27 dB on O‑HAZE, +1.65 dB on HazyDet, and increasing SSIM by +0.124.

Face shadow removal (FaceShadow): LearnIR led on both synthetic and real data, raising PSNR by +2.44 dB and +1.71 dB respectively.

Ablation Study

Removing DPSC caused a PSNR drop of 4.4 dB, confirming the importance of posterior‑sampling correction. Removing DRM reduced PSNR by 1.27 dB, highlighting the role of dynamic resolution in preserving global structure. Omitting both modules collapsed performance to 22.86 dB, demonstrating their synergistic effect.

Computational Efficiency

DRM’s non‑trainable bilinear interpolation adds virtually zero overhead. The full model requires only 5 sampling steps, with total inference time around 1.6 seconds.

Visual Results

Below are example outputs (original vs. restored) for shadow removal, dehazing, and face shadow removal.