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Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear…

Machine Learning · Statistics 2021-11-02 Agnimitra Dasgupta , Zichao Wendy Di

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Machine Learning · Computer Science 2023-05-16 Jaemoo Choi , Yesom Park , Myungjoo Kang

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…

Machine Learning · Computer Science 2021-07-02 Jay Whang , Qi Lei , Alexandros G. Dimakis

How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…

Computer Vision and Pattern Recognition · Computer Science 2020-11-17 Zhaoqun Li

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…

Machine Learning · Computer Science 2026-02-02 Katherine Keegan , Lars Ruthotto

Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of…

Machine Learning · Computer Science 2017-11-08 Kevin Roth , Aurelien Lucchi , Sebastian Nowozin , Thomas Hofmann

High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing…

Information Theory · Computer Science 2025-12-24 Yuntong Gu , Xiangming meng , Zhiyuan Lin , Sheng Wu , Linling Kuang

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based…

Machine Learning · Computer Science 2025-04-23 Asad Aali , Marius Arvinte , Sidharth Kumar , Jonathan I. Tamir

Recent image restoration methods can be broadly categorized into two classes: (1) regression methods that recover the rough structure of the original image without synthesizing high-frequency details and (2) generative methods that…

Computer Vision and Pattern Recognition · Computer Science 2024-01-02 Hwayoon Lee , Kyoungkook Kang , Hyeongmin Lee , Seung-Hwan Baek , Sunghyun Cho

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Computer Vision and Pattern Recognition · Computer Science 2024-04-17 Bowen Song , Soo Min Kwon , Zecheng Zhang , Xinyu Hu , Qing Qu , Liyue Shen

We propose MoNoise: a normalization model focused on generalizability and efficiency, it aims at being easily reusable and adaptable. Normalization is the task of translating texts from a non- canonical domain to a more canonical domain, in…

Computation and Language · Computer Science 2017-10-11 Rob van der Goot , Gertjan van Noord

Contemporary text-to-image models exhibit a surprising degree of mode collapse, as can be seen when sampling several images given the same text prompt. Previous work has attempted to address this issue by steering the model using guidance…

Computer Vision and Pattern Recognition · Computer Science 2026-05-04 Anne Harrington , A. Sophia Koepke , Shyamgopal Karthik , Trevor Darrell , Alexei A. Efros

The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images is to combine the forward and backward diffusion equations. However, the latter problem is well known to be exponentially…

Numerical Analysis · Mathematics 2023-06-13 Vo Anh Khoa , Mai Thanh Nhat Truong , Imhotep Hogan , Roselyn Williams

The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…

Signal Processing · Electrical Eng. & Systems 2025-01-08 Tamir Bendory , Dan Edidin

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Machine Learning · Statistics 2019-06-06 Zachary M. Ziegler , Alexander M. Rush

Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…

Numerical Analysis · Mathematics 2025-10-21 Clemens Arndt , Judith Nickel

We propose a diffusion-based inverse rendering framework that decomposes a single RGB image into geometry, material, and lighting. Inverse rendering is inherently ill-posed, making it difficult to predict a single accurate solution. To…

Computer Vision and Pattern Recognition · Computer Science 2025-03-14 JunYong Choi , Min-Cheol Sagong , SeokYeong Lee , Seung-Won Jung , Ig-Jae Kim , Junghyun Cho

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Numerical Analysis · Mathematics 2024-03-19 Simon Arridge , Andreas Hauptmann , Yury Korolev

Generative models have fundamentally reshaped the landscape of decision-making, reframing the problem from pure scalar reward maximization to high-fidelity trajectory generation and distribution matching. This paradigm shift addresses…