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Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…

Machine Learning · Computer Science 2026-04-02 Giovanni Conforti , Alain Durmus , Le-Tuyet-Nhi Pham , Gael Raoul

The evolution of semantic segmentation has long been dominated by learning more discriminative image representations for classifying each pixel. Despite the prominent advancements, the priors of segmentation masks themselves, e.g.,…

Computer Vision and Pattern Recognition · Computer Science 2023-06-23 Zeqiang Lai , Yuchen Duan , Jifeng Dai , Ziheng Li , Ying Fu , Hongsheng Li , Yu Qiao , Wenhai Wang

Analytical diffusion models offer a mathematically transparent path to generative modeling by formulating the denoising score as an empirical-Bayes posterior mean. However, this interpretability comes at a prohibitive cost: the standard…

Machine Learning · Computer Science 2026-02-19 Xinyi Shang , Peng Sun , Jingyu Lin , Zhiqiang Shen

Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain…

Machine Learning · Computer Science 2024-09-16 Hang Li , Wei Jin , Geri Skenderi , Harry Shomer , Wenzhuo Tang , Wenqi Fan , Jiliang Tang

Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later…

Computer Vision and Pattern Recognition · Computer Science 2026-05-21 Howard Xiao , Brian Chao , Lior Yariv , Gordon Wetzstein

Diffusion models have shown promising results for a wide range of generative tasks with continuous data, such as image and audio synthesis. However, little progress has been made on using diffusion models to generate discrete symbolic music…

Sound · Computer Science 2023-10-24 Jincheng Zhang , György Fazekas , Charalampos Saitis

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…

Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…

Machine Learning · Computer Science 2025-04-30 Hao Luan , See-Kiong Ng , Chun Kai Ling

Based on the Denoising Diffusion Probabilistic Model (DDPM), medical image segmentation can be described as a conditional image generation task, which allows to compute pixel-wise uncertainty maps of the segmentation and allows an implicit…

Image and Video Processing · Electrical Eng. & Systems 2022-11-01 Xutao Guo , Yanwu Yang , Chenfei Ye , Shang Lu , Yang Xiang , Ting Ma

Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…

Machine Learning · Computer Science 2024-09-04 Solveig Klepper

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

Machine Learning · Computer Science 2025-08-14 Tristan S. W. Stevens , Hans van Gorp , Faik C. Meral , Junseob Shin , Jason Yu , Jean-Luc Robert , Ruud J. G. van Sloun

Learning to generate graphs is challenging as a graph is a set of pairwise connected, unordered nodes encoding complex combinatorial structures. Recently, several works have proposed graph generative models based on normalizing flows or…

Machine Learning · Computer Science 2023-06-21 Xiaohui Chen , Yukun Li , Aonan Zhang , Li-Ping Liu

While Diffusion Generative Models have achieved great success on image generation tasks, how to efficiently and effectively incorporate them into speech generation especially translation tasks remains a non-trivial problem. Specifically,…

Computation and Language · Computer Science 2023-10-27 Yongxin Zhu , Zhujin Gao , Xinyuan Zhou , Zhongyi Ye , Linli Xu

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations…

Chemical Physics · Physics 2019-01-30 Joseph F. Rudzinski , Marc Radu , Tristan Bereau

We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…

Machine Learning · Computer Science 2024-10-31 Yuxuan Gu , Xiaocheng Feng , Lei Huang , Yingsheng Wu , Zekun Zhou , Weihong Zhong , Kun Zhu , Bing Qin

Large denoising diffusion models, such as Stable Diffusion, have been trained on billions of image-caption pairs to perform text-conditioned image generation. As a byproduct of this training, these models have acquired general knowledge…

Computer Vision and Pattern Recognition · Computer Science 2025-10-07 Alexandros Graikos , Nebojsa Jojic , Dimitris Samaras

We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…

Computer Vision and Pattern Recognition · Computer Science 2025-08-05 Bicheng Xu , Qi Yan , Renjie Liao , Lele Wang , Leonid Sigal

We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts…

Machine Learning · Computer Science 2026-05-12 Chaitanya Amballa , Sattwik Basu , Jorge Vančo Sampedro , Romit Roy Choudhury

Recent advances in Graph Neural Networks (GNNs) have revolutionized graph-structured data modeling, yet traditional GNNs struggle with complex heterogeneous structures prevalent in real-world scenarios. Despite progress in handling…

Machine Learning · Computer Science 2025-01-07 Zongwei Li , Lianghao Xia , Hua Hua , Shijie Zhang , Shuangyang Wang , Chao Huang

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…

Machine Learning · Computer Science 2024-07-25 Jian Xu , Delu Zeng , John Paisley