Organizations: Indian Institute of Technology Tirupati, India.
Abstract
In recent times, diffusion models have achieved remarkable performance in image restoration tasks. Their core mechanism relies on the restricted presumption of degradation prior to the additive noise operation. However, the blur model, one of the most widely studied degradation formulations, violates this assumption, as it is inherently based on convolution rather than addition. In this paper, we introduce ConvDiff, a novel diffusion based framework that substitutes the additive operation with convolution for the task of image deblurring. In the forward process, we construct a meaningful trajectory from the clean image to its blurred counterpart by exploiting the frequency domain characteristics of convolution, rather than progressively corrupting the image with additive noise. While the current work instantiates this framework for Gaussian blur, where frequency-domain decomposition yields closed-form and physically valid intermediate states, the underlying principle of constructing degradation trajectories from the blur operator extends naturally to other blur families. This formulation bridges the gap between the mathematical principles of blurring and the iterative design of diffusion-based restoration algorithms, enabling more physically grounded and effective image restoration models.
Generative flow models offer powerful priors learned from large-scale natural images, but directly adapting them to restoration tasks such as motion deblurring causes severe fidelity degradation, as their training objective is inherently misaligned with restoration. We present DeblurFlow, a framework that resolves this misalignment by reformulating the flow trajectory itself: we replace the noise endpoint with the blur observation, which makes the underlying vector field coincide with the residual error between blur and clean images. Under this formulation, the standard flow matching loss naturally takes the form of a residual loss, allowing pretrained flow models to be optimized under restoration-aligned objectives via LoRA adaptation. This formulation further enables a dual-expert sampling strategy: a fidelity expert provides a high-fidelity initialization, e.g., PSNR 33.69 dB, and DeblurFlow enhances perceptual quality with only a marginal fidelity reduction to 33.05 dB, whereas directly applying a generative model on top of a fidelity expert decreases PSNR to 27.60 dB. To make this practical, we further introduce r-space, a latent space tailored for residual decoding rather than image reconstruction, which reduces encoder-decoder cost by up to 9×over standard VAE latents. Extensive experiments on GoPro, HIDE, RealBlur, and RWBI demonstrate that DeblurFlow achieves strong restoration fidelity and perceptual realism, while remaining computationally practical.
Existing diffusion-based methods have recently made significant progress in image dehazing. However, they typically neglect the physics of haze formation and reconstruct clean images from pure Gaussian noise, thereby limiting their restoration potential. To address this issue, we propose Haze-Noise Diffusion (HNDiff), a novel diffusion framework that embeds the atmospheric scattering model as an inductive bias. By grounding diffusion in physical principles, HNDiff ensures that the restoration aligns more closely with underlying mechanisms of haze formation. In its forward process, we introduce joint haze-noise diffusion with a haze-aware noise scheduler, which progressively adds both haze and noise to an image. Essentially, the scheduler adapts noise levels according to haze density, meaning that regions with heavier haze receive stronger noise injection to encourage content generation, while clearer regions receive lighter noise to better preserve details, which directly links the forward degradation process with the physics of haze. In the reverse process, we then derive a physically consistent dehazing-denoising process that simultaneously removes haze and noise to restore a clean image in a manner aligned with the forward degradation process. To further enhance practicality, we propose Latent HNDiff, which compiles clean latent priors that can be seamlessly integrated into existing dehazing networks to boost performance. Extensive experiments show that our work significantly improves leading dehazing backbones and achieves state-of-the-art results on benchmark datasets. The project page is available at https://jin-ting-he.github.io/HNDiff .
Defocus deblurring in pathological microscopy remains challenging due to the spatially varying and locally discontinuous nature of optical blur induced by a position-dependent integral imaging process. Existing deep learning methods, constrained by shift-invariance assumptions and limited interpretability, are not well suited to such heterogeneous blur patterns. Neural operators provide a principled alternative by modeling defocus formation directly as an integral operator, offering a new perspective on defocus deblurring. However, most existing neural operator architectures for low-level vision rely on globally parameterized kernels that assume smoothness and stationarity, limiting their ability to model heterogeneous and locally discontinuous blur patterns. To address this limitation, we propose the Discontinuous Galerkin Neural Operator (DGNO), which parameterizes the integral kernel using a discontinuous Galerkin formulation with element-local volume operators and interface numerical fluxes. DGNO provides a principled combination of locality, heterogeneity modeling, and global coherence while preserving the underlying physics of optical image formation. Extensive and insightful experiments demonstrate that DGNO surpasses state-of-the-arts, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance. The code will be released at https://github.com/DeepMed-Lab-ECNU/Single-Image-Deblur.