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Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…

Numerical Analysis · Mathematics 2021-11-23 Alex Viguerie , Silvia Bertoluzza , Alessandro Veneziani , Ferdinando Auricchio

Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel…

Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs…

Machine Learning · Computer Science 2025-05-01 Kaiwen Zheng , Guande He , Jianfei Chen , Fan Bao , Jun Zhu

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from…

Machine Learning · Computer Science 2025-06-02 Heli Ben-Hamu , Itai Gat , Daniel Severo , Niklas Nolte , Brian Karrer

The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…

Probability · Mathematics 2018-05-31 Arnab Ganguly , P. Sundar

Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due…

Machine Learning · Computer Science 2026-04-21 Marcel Kollovieh , Sirine Ayadi , Stephan Günnemann

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of…

Machine Learning · Computer Science 2025-05-20 Cheng Lu , Yuhao Zhou , Fan Bao , Jianfei Chen , Chongxuan Li , Jun Zhu

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…

Machine Learning · Computer Science 2024-06-04 Grigory Bartosh , Dmitry Vetrov , Christian A. Naesseth

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement…

Machine Learning · Computer Science 2026-05-04 Hasan Amin , Yuan Gao , Yaser Souri , Subhojit Som , Ming Yin , Rajiv Khanna , Xia Song

Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…

Machine Learning · Computer Science 2024-05-24 Lorenz Richter , Julius Berner

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…

Machine Learning · Computer Science 2026-01-16 Khashayar Gatmiry , Sitan Chen , Adil Salim

As Diffusion Models have shown promising performance, a lot of efforts have been made to improve the controllability of Diffusion Models. However, how to train Diffusion Models to have the disentangled latent spaces and how to naturally…

Computer Vision and Pattern Recognition · Computer Science 2025-07-02 Wonwoong Cho , Hareesh Ravi , Midhun Harikumar , Vinh Khuc , Krishna Kumar Singh , Jingwan Lu , David I. Inouye , Ajinkya Kale

We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either…

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…

Machine Learning · Computer Science 2026-05-22 Yunshu Wu , Jiayi Cheng , Longxuan Yu , Partha Thakuria , Rob Brekelmans , Evangelos E. Papalexakis , Greg Ver Steeg

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…

Machine Learning · Computer Science 2026-05-22 Yunshu Wu , Jiayi Cheng , Longxuan Yu , Partha Thakuria , Rob Brekelmans , Evangelos E. Papalexakis , Greg Ver Steeg

Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al.…

Machine Learning · Computer Science 2024-08-13 Lingxiao Zhao , Xueying Ding , Lijun Yu , Leman Akoglu

Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…

Machine Learning · Computer Science 2026-02-02 Juhyeok Choi , Chenglin Fan

Diffusion models have demonstrated impressive generative capabilities, but their \textit{exposure bias} problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically…

Machine Learning · Computer Science 2024-04-12 Mang Ning , Mingxiao Li , Jianlin Su , Albert Ali Salah , Itir Onal Ertugrul

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…

Numerical Analysis · Mathematics 2012-04-10 Max Duarte , Zdenek Bonaventura , Marc Massot , Anne Bourdon , Stéphane Descombes , Thierry Dumont

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…

Statistics Theory · Mathematics 2026-02-18 Armand Gissler , Saeed Saremi , Francis Bach