SP^3: Spherical Priors for Plug-and-Play Restoration

Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.

MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations. To stabilize reconstruction optimization and suppress INR-induced artifacts, we further propose an explicit sparse proximal regularization (e.g., $\ell_0$-type) applied directly in the high-resolution image domain, which discourages spurious high-frequency patterns while preserving sharp structures. The resulting optimization is solved efficiently via a multi-grade proximal alternating scheme, and we establish convergence guarantees for the associated updates under standard regularity conditions. Experiments on mixed-degradation benchmarks demonstrate that MG-SpaIR consistently outperforms strong training-data-free baselines such as Deep Image Prior, providing a stable, interpretable, and data-efficient alternative to conventional learning-based restoration methods.

Image restoration seeks to recover high-quality images from degraded inputs but becomes highly ill-posed under complex, mixed degradations. While unified all-in-one models are common, their performance declines as degradation complexity increases. Recent works adopt Chain-of-Thought (CoT) reasoning for multi-round restoration using specialized modules. However, this approach faces two key limitations: (i) increased computational cost due to multi-step processing, and (ii) weak modeling of interactions between degradations during stepwise inference. We introduce CoTIR, a universal image restoration framework that internalizes CoT reasoning within a single model. Concretely, we view image restoration as a specialized subtask of image editing, which implies that a large-scale pre-trained editing model provides a more favorable optimization starting point. Building on this, we fine-tune the model for restoration and further encode structured CoT-style reasoning into the learning objective via a differentiable formulation inspired by Lagrangian optimization, enabling holistic restoration without chaining specialized restorers. To facilitate training and evaluation, we further present CoTIR-Bench, a large-scale benchmark comprising 5.2 million samples with CoT-style reasoning traces. Extensive experiments on CoTIR-Bench and broad real composite degradation scenes show that CoTIR achieves stronger perceptual quality and more competitive fidelity than both all-in-one models and multi-round restoration methods. The source code is available at https://github.com/gy65896/CoTIR.