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Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…

Methodology · Statistics 2021-07-19 Jared M. Clark , Richard L. Warr

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

Image and Video Processing · Electrical Eng. & Systems 2025-08-22 Idan Achituve , Hai Victor Habi , Amir Rosenfeld , Arnon Netzer , Idit Diamant , Ethan Fetaya

We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…

Machine Learning · Computer Science 2026-05-28 Andrew Millard , Fredrik Lindsten , Zheng Zhao

We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…

Methodology · Statistics 2014-12-01 Sergios Agapiou , Gareth O. Roberts , Sebastian J. Vollmer

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…

Machine Learning · Computer Science 2024-11-19 William Huang , Yifeng Jiang , Tom Van Wouwe , C. Karen Liu

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

Machine Learning · Computer Science 2024-10-31 Qidong Yang , Weicheng Zhu , Joseph Keslin , Laure Zanna , Tim G. J. Rudner , Carlos Fernandez-Granda

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary…

Computer Vision and Pattern Recognition · Computer Science 2024-07-17 Soobin Um , Jong Chul Ye

Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…

Computer Vision and Pattern Recognition · Computer Science 2023-01-31 Gyeongnyeon Kim , Wooseok Jang , Gyuseong Lee , Susung Hong , Junyoung Seo , Seungryong Kim

We argue that diffusion models' success in modeling complex distributions is, for the most part, coming from their input conditioning. This paper investigates the representation used to condition diffusion models from the perspective that…

Computer Vision and Pattern Recognition · Computer Science 2026-01-07 Samuel Lavoie , Michael Noukhovitch , Aaron Courville

Diffusion models without guidance generate very unrealistic samples. Guidance is used ubiquitously, and previous research has attributed its effect to low-temperature sampling that improves quality by trading off diversity. However, this…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Shanchuan Lin , Xiao Yang

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

Machine Learning · Computer Science 2023-08-21 Francisco Vargas , Will Grathwohl , Arnaud Doucet

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

Machine Learning · Computer Science 2025-08-25 Sebastian Sanokowski , Sepp Hochreiter , Sebastian Lehner

We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…

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

This paper introduces the Sequential Monte Carlo Transformer, an original approach that naturally captures the observations distribution in a transformer architecture. The keys, queries, values and attention vectors of the network are…

Machine Learning · Computer Science 2020-12-16 Alice Martin , Charles Ollion , Florian Strub , Sylvain Le Corff , Olivier Pietquin

We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…

Machine Learning · Statistics 2025-05-14 Hoang Tran , Zezhong Zhang , Feng Bao , Dan Lu , Guannan Zhang

Diffusion models have demonstrated superior performance across various generative tasks including images, videos, and audio. However, they encounter difficulties in directly generating high-resolution samples. Previously proposed solutions…

Computer Vision and Pattern Recognition · Computer Science 2024-04-03 Juno Hwang , Yong-Hyun Park , Junghyo Jo

Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm…

Computation and Language · Computer Science 2026-05-19 Lize Shao , Michael Cardei , Zichen Xie , Ferdinando Fioretto , Wenxi Wang

Discrete diffusion models have recently emerged as a powerful class of generative models for chemistry and biology data. In these fields, the goal is to generate various samples with high rewards (e.g., drug-likeness in molecules), making…

Machine Learning · Computer Science 2026-02-11 Prin Phunyaphibarn , Minhyuk Sung

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…

Machine Learning · Computer Science 2024-12-09 Zixiang Chen , Huizhuo Yuan , Yongqian Li , Yiwen Kou , Junkai Zhang , Quanquan Gu