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The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…

Numerical Analysis · Mathematics 2020-06-18 Leif Bergerhoff , Marcelo Cárdenas , Joachim Weickert , Martin Welk

Diffusion models can be used as learned priors for solving various inverse problems. However, most existing approaches are restricted to linear inverse problems, limiting their applicability to more general cases. In this paper, we build…

Image and Video Processing · Electrical Eng. & Systems 2022-11-28 Bahjat Kawar , Jiaming Song , Stefano Ermon , Michael Elad

Diffusion models have demonstrated great potential in generating high-quality content for images, natural language, protein domains, etc. However, how to perform user-preferred targeted generation via diffusion models with only black-box…

Machine Learning · Statistics 2024-06-11 Yueming Lyu , Kim Yong Tan , Yew Soon Ong , Ivor W. Tsang

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be…

Computer Vision and Pattern Recognition · Computer Science 2022-11-22 Hyungjin Chung , Jeongsol Kim , Sehui Kim , Jong Chul Ye

Rendering and inverse rendering are pivotal tasks in both computer vision and graphics. The rendering equation is the core of the two tasks, as an ideal conditional distribution transfer function from intrinsic properties to RGB images.…

Computer Vision and Pattern Recognition · Computer Science 2025-03-06 Zhifei Chen , Tianshuo Xu , Wenhang Ge , Leyi Wu , Dongyu Yan , Jing He , Luozhou Wang , Lu Zeng , Shunsi Zhang , Yingcong Chen

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…

Computer Vision and Pattern Recognition · Computer Science 2024-05-20 Hanyu Chen , Zhixiu Hao , Liying Xiao

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

Machine Learning · Statistics 2025-06-09 Jakiw Pidstrigach , Youssef Marzouk , Sebastian Reich , Sven Wang

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…

Numerical Analysis · Mathematics 2024-10-29 Xiang Cao , Xiaoqun Zhang

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…

Machine Learning · Statistics 2024-10-17 Yingqing Guo , Hui Yuan , Yukang Yang , Minshuo Chen , Mengdi Wang

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by…

Computer Vision and Pattern Recognition · Computer Science 2023-10-26 Hyungjin Chung , Jeongsol Kim , Jong Chul Ye

Recent advances in image editing with diffusion models have achieved impressive results, offering fine-grained control over the generation process. However, these methods are computationally intensive because of their iterative nature.…

Computer Vision and Pattern Recognition · Computer Science 2025-06-25 Ilia Beletskii , Andrey Kuznetsov , Aibek Alanov

We demonstrate an image dequantizing diffusion model that enables novel edits on natural images. We propose operating on quantized images because they offer easy abstraction for patch-based edits and palette transfer. In particular, we show…

Computer Vision and Pattern Recognition · Computer Science 2025-01-24 Vaibhav Vavilala , Faaris Shaik , David Forsyth

Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…

Numerical Analysis · Mathematics 2015-07-13 Martin Burger , Ole Loseth Elvetun , Matthias Schlottbom

Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…

Computer Vision and Pattern Recognition · Computer Science 2021-04-02 Linjie Lyu , Marc Habermann , Lingjie Liu , Mallikarjun B R , Ayush Tewari , Christian Theobalt

Diffusion models have shown significant progress in image translation tasks recently. However, due to their stochastic nature, there's often a trade-off between style transformation and content preservation. Current strategies aim to…

Computer Vision and Pattern Recognition · Computer Science 2023-06-08 Gihyun Kwon , Jong Chul Ye

Many image processing problems are naturally expressed as energy minimization or shape optimization problems, in which the free variable is a shape, such as a curve in 2d or a surface in 3d. Examples are image segmentation, multiview stereo…

Optimization and Control · Mathematics 2013-07-23 Günay Doğan

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…

Computational Physics · Physics 2025-08-05 Jiyong Kim , Sunwoong Yang , Namwoo Kang

Text-guided diffusion models have revolutionized image generation and editing, offering exceptional realism and diversity. Specifically, in the context of diffusion-based editing, where a source image is edited according to a target prompt,…

Computer Vision and Pattern Recognition · Computer Science 2023-10-20 Xuan Ju , Ailing Zeng , Yuxuan Bian , Shaoteng Liu , Qiang Xu

We consider the inverse problem of denoising an image where each point (pixel) is an element of a target set, which we refer to as a target-valued image. The target sets considered are either (i) a closed convex set of Euclidean space or…

Numerical Analysis · Mathematics 2018-06-20 Braxton Osting , Dong Wang
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