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prior regularization

Prior regularization is a technique in machine learning, statistics, and inverse problem solving that incorporates prior knowledge or an assumed probability distribution into an optimization objective to constrain solutions and prevent overfitting. Grounded in Bayesian principles, it operates by pairing a data-fidelity term, which measures consistency with observed evidence, with a regularization penalty derived from a prior distribution over plausible states or parameters. This penalty guides the estimation or generative process toward solutions that conform to expected data characteristics, such as smoothness, structural consistency, or learned natural distributions. By biasing the optimization toward likely configurations, prior regularization stabilizes ill-posed tasks and ensures that reconstructed or estimated outputs remain coherent with established domain distributions.

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Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models

Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models

Guanhua Zhang, Jiabao Ji, Yang Zhang, Mo Yu, Tommi S. Jaakkola, Shiyu Chang

OrganizationsIBMMassachusetts Institute of TechnologyMIT-IBM Watson AI LabUniversity of California, Santa Barbara

Why you should read this

Proposes CoPaint, a Bayesian framework for diffusion-based image inpainting that jointly modifies revealed and unrevealed regions to eliminate incoherence while driving approximation errors to zero to strictly match reference constraints.

Image inpainting refers to the task of generating a complete, natural image based on a partially revealed reference image. Recently, many research interests have been focused on addressing this problem using fixed diffusion models. These approaches typically directly replace the revealed region of the intermediate or final generated images with that of the reference image or its variants. However, since the unrevealed regions are not directly modified to match the context, it results in incoherence between revealed and unrevealed regions. To address the incoherence problem, a small number of methods introduce a rigorous Bayesian framework, but they tend to introduce mismatches between the generated and the reference images due to the approximation errors in computing the posterior distributions. In this paper, we propose CoPaint, which can coherently inpaint the whole image without introducing mismatches. CoPaint also uses the Bayesian framework to jointly modify both revealed and unrevealed regions, but approximates the posterior distribution in a way that allows the errors to gradually drop to zero throughout the denoising steps, thus strongly penalizing any mismatches with the reference image. Our experiments verify that CoPaint can outperform the existing diffusion-based methods under both objective and subjective metrics. The codes are available at https://github.com/UCSB-NLP-Chang/CoPaint/.

Added

2026-09-26