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The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…

Data Analysis, Statistics and Probability · Physics 2017-08-04 Ronen Talmon , Hau-tieng Wu

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Machine Learning · Computer Science 2025-04-22 Dimitris G. Giovanis , Ellis Crabtree , Roger G. Ghanem , Ioannis G. Kevrekidis

The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand…

Computational Physics · Physics 2020-11-25 Michele Invernizzi , Pablo Miguel Piaggi , Michele Parrinello

Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…

Machine Learning · Computer Science 2026-05-08 Matias G. Delgadino , Sebastien Motsch , Advait Parulekar , William Porteous , Sanjay Shakkottai

Discrete diffusion models have recently emerged as a promising alternative to the autoregressive approach for generating discrete sequences. Sample generation via gradual denoising or demasking processes allows them to capture hierarchical…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

Machine Learning · Computer Science 2018-11-13 Rohitash Chandra , Konark Jain , Ratneel V. Deo , Sally Cripps

Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly…

Machine Learning · Statistics 2023-09-08 Huangjie Zheng , Pengcheng He , Weizhu Chen , Mingyuan Zhou

While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and…

Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality…

Machine Learning · Computer Science 2024-11-05 Yunshu Wu , Yingtao Luo , Xianghao Kong , Evangelos E. Papalexakis , Greg Ver Steeg

Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method…

Machine Learning · Statistics 2025-05-28 Dongze Wu , Yao Xie

Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has…

Simulated annealing solves global optimization problems by means of a random walk in a cooling energy landscape based on the objective function and a temperature parameter. However, if the temperature is decreased too quickly, this…

Optimization and Control · Mathematics 2025-04-14 Vincent Molin , Axel Ringh , Moritz Schauer , Akash Sharma

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Machine Learning · Computer Science 2023-11-10 Anshuk Uppal , Kristoffer Stensbo-Smidt , Wouter Boomsma , Jes Frellsen

The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence…

Quantitative Methods · Quantitative Biology 2020-04-03 Maxime Woringer , Ignacio Izeddin , Cyril Favard , Hugues Berry

Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between…

Machine Learning · Statistics 2023-10-10 Omar Chehab , Aapo Hyvarinen , Andrej Risteski

We propose a sampling-based framework for finite-horizon trajectory and policy optimization under differentiable dynamics by casting controller design as inference. Specifically, we minimize a KL-regularized expected trajectory cost, which…

Machine Learning · Computer Science 2026-05-12 Heng Yang

Diffusion models have recently emerged as the dominant approach in visual generation tasks. However, the lengthy denoising chains and the computationally intensive noise estimation networks hinder their applicability in low-latency and…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Qian Zeng , Jie Song , Yuanyu Wan , Huiqiong Wang , Mingli Song

Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire…

Statistics Theory · Mathematics 2013-03-14 Nicolas Chauffert , Philippe Ciuiu , Jonas Kahn , Pierre Weiss

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…

Computation · Statistics 2025-11-04 Paula Cordero-Encinar , Andrew B. Duncan , Sebastian Reich , O. Deniz Akyildiz

The remarkable performance of deep neural networks depends on the availability of massive labeled data. To alleviate the load of data annotation, active deep learning aims to select a minimal set of training points to be labelled which…

Machine Learning · Computer Science 2020-03-24 Dan Kushnir , Luca Venturi