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The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability…

人工智能 · 计算机科学 2022-12-29 Sarah Boufelja Y. , Anthony Quinn , Martin Corless , Robert Shorten

The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…

一般拓扑 · 数学 2025-07-03 Yuping Lv , Qi Zhao , Xuebin Chang , Wei Zeng

The embedded topic model (ETM) is a widely used approach that assumes the sampled document-topic distribution conforms to the logistic normal distribution for easier optimization. However, this assumption oversimplifies the real…

计算与语言 · 计算机科学 2025-01-03 Wei Shao , Mingyang Liu , Linqi Song

Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current…

机器人学 · 计算机科学 2025-01-03 Julia Briden , Breanna Johnson , Richard Linares , Abhishek Cauligi

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…

最优化与控制 · 数学 2026-05-28 Gabriel Peyré

Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…

计算机视觉与模式识别 · 计算机科学 2024-12-30 Xiaoping Wu , Jie Hu , Xiaoming Wei

Flow-matching models have recently emerged as a powerful framework for continuous generative modeling, including 3D point cloud synthesis. However, their deployment is limited by the need for multiple sequential sampling steps at inference…

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…

图像与视频处理 · 电气工程与系统科学 2022-11-01 Xutao Guo , Yanwu Yang , Chenfei Ye , Shang Lu , Yang Xiang , Ting Ma

We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…

机器学习 · 统计学 2025-11-07 Aimee Maurais , Bamdad Hosseini , Youssef Marzouk

Diffusion models have demonstrated strong performance in sampling and editing multi-modal data with high generation quality, yet they suffer from the iterative generation process which is computationally expensive and slow. In addition,…

计算机视觉与模式识别 · 计算机科学 2024-06-19 Xinrui Zu , Qian Tao

Diffusion policies have shown promise in learning complex behaviors from demonstrations, particularly for tasks requiring precise control and long-term planning. However, they face challenges in robustness when encountering distribution…

机器学习 · 计算机科学 2025-02-24 Mingyang Sun , Pengxiang Ding , Weinan Zhang , Donglin Wang

Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…

计算机视觉与模式识别 · 计算机科学 2024-08-27 Xuyi Yu

The Dual Diffusion Implicit Bridge (DDIB) is an emerging image-to-image (I2I) translation method that preserves cycle consistency while achieving strong flexibility. It links two independently trained diffusion models (DMs) in the source…

计算机视觉与模式识别 · 计算机科学 2025-11-17 Zhanpeng Wang , Shuting Cao , Yuhang Lu , Yuhan Li , Na Lei , Zhongxuan Luo

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…

机器学习 · 计算机科学 2023-12-13 Yuxuan Song , Jingjing Gong , Minkai Xu , Ziyao Cao , Yanyan Lan , Stefano Ermon , Hao Zhou , Wei-Ying Ma

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…

机器学习 · 计算机科学 2024-06-04 Grigory Bartosh , Dmitry Vetrov , Christian A. Naesseth

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…

机器学习 · 计算机科学 2024-06-04 Anjian Li , Zihan Ding , Adji Bousso Dieng , Ryne Beeson

An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…

最优化与控制 · 数学 2025-07-28 Jacob J. M. Francis , Colin J. Cotter , Marion P. Mittermaier

In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…

统计理论 · 数学 2025-06-25 Sivaraman Balakrishnan , Tudor Manole , Larry Wasserman

When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…

机器学习 · 计算机科学 2024-01-23 Chuanwen Feng , Wenlong Chen , Ao Ke , Yilong Ren , Xike Xie , S. Kevin Zhou

In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…

机器学习 · 计算机科学 2021-04-06 Karthik S. Gurumoorthy , Pratik Jawanpuria , Bamdev Mishra