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We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Machine Learning · Computer Science 2024-11-04 Jiahe Huang , Guandao Yang , Zichen Wang , Jeong Joon Park

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor…

Machine Learning · Statistics 2018-02-26 Viraj Shah , Chinmay Hegde

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

Machine Learning · Computer Science 2026-03-31 Nihal Sanjay Singh , Mazdak Mohseni-Rajaee , Shaila Niazi , Kerem Y. Camsari

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…

Numerical Analysis · Mathematics 2020-04-02 Jerome Droniou , Kim-Ngan Le

Image diffusion models, trained on massive image collections, have emerged as the most versatile image generator model in terms of quality and diversity. They support inverting real images and conditional (e.g., text) generation, making…

Computer Vision and Pattern Recognition · Computer Science 2023-03-23 Duygu Ceylan , Chun-Hao Paul Huang , Niloy J. Mitra

The recent wave of large-scale text-to-image diffusion models has dramatically increased our text-based image generation abilities. These models can generate realistic images for a staggering variety of prompts and exhibit impressive…

Machine Learning · Computer Science 2023-09-14 Alexander C. Li , Mihir Prabhudesai , Shivam Duggal , Ellis Brown , Deepak Pathak

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…

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

Recent inverse problem solvers that leverage generative diffusion priors have garnered significant attention due to their exceptional quality. However, adaptation of the prior is necessary when there exists a discrepancy between the…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Hyungjin Chung , Jong Chul Ye

Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we…

Machine Learning · Computer Science 2024-10-04 Mathis Gerdes , Max Welling , Miranda C. N. Cheng

It is a known problem that deep-learning-based end-to-end (E2E) channel coding systems depend on a known and differentiable channel model, due to the learning process and based on the gradient-descent optimization methods. This places the…

Information Theory · Computer Science 2023-11-30 Muah Kim , Rick Fritschek , Rafael F. Schaefer

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

Machine Learning · Computer Science 2022-10-26 Sarthak Mittal , Guillaume Lajoie , Stefan Bauer , Arash Mehrjou

Diffusion models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…

Computer Vision and Pattern Recognition · Computer Science 2025-07-01 Shijie Zhou , Huaisheng Zhu , Rohan Sharma , Jiayi Chen , Ruiyi Zhang , Kaiyi Ji , Changyou Chen

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have…

Computation and Language · Computer Science 2023-04-11 Jiaao Chen , Aston Zhang , Mu Li , Alex Smola , Diyi Yang

While diffusion models excel at generating continuous data such as images, adapting them to discrete tasks has relied on indirect approaches that either operate in continuous embedding spaces or use token masking mechanisms, both of which…

Computer Vision and Pattern Recognition · Computer Science 2025-11-25 Xiao Li , Jiaqi Zhang , Shuxiang Zhang , Tianshui Chen , Liang Lin , Guangrun Wang

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

Machine Learning · Computer Science 2025-04-07 Luis Barba , Johannes Kirschner , Tomas Aidukas , Manuel Guizar-Sicairos , Benjamín Béjar

We introduce the Multi-Motion Discrete Diffusion Models (M2D2M), a novel approach for human motion generation from textual descriptions of multiple actions, utilizing the strengths of discrete diffusion models. This approach adeptly…

Computer Vision and Pattern Recognition · Computer Science 2024-07-22 Seunggeun Chi , Hyung-gun Chi , Hengbo Ma , Nakul Agarwal , Faizan Siddiqui , Karthik Ramani , Kwonjoon Lee

Latent dynamical models are commonly used to learn the distribution of a latent dynamical process that represents a sequence of noisy data samples. However, producing samples from such models with high fidelity is challenging due to the…

Machine Learning · Computer Science 2023-08-17 Mohammad R. Rezaei

Diffusion models learn strong image priors that can be leveraged to solve inverse problems like medical image reconstruction. However, for real-world applications such as 3D Computed Tomography (CT) imaging, directly training diffusion…

Computer Vision and Pattern Recognition · Computer Science 2025-12-23 Taewon Yang , Jason Hu , Jeffrey A. Fessler , Liyue Shen

Recent advances in diffusion models have demonstrated remarkable capabilities in video generation. However, the computational intensity remains a significant challenge for practical applications. While feature caching has been proposed to…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Xuran Ma , Yexin Liu , Yaofu Liu , Xianfeng Wu , Mingzhe Zheng , Zihao Wang , Ser-Nam Lim , Harry Yang