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We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Machine Learning · Computer Science 2026-05-11 Aditya Ranganath , Mukesh Singhal

In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…

Machine Learning · Computer Science 2025-08-14 Gen Li , Yuchen Zhou , Yuting Wei , Yuxin Chen

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Machine Learning · Statistics 2024-03-08 Gen Li , Yuting Wei , Yuxin Chen , Yuejie Chi

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

Machine Learning · Statistics 2026-04-24 Saptarshi Chakraborty , Quentin Berthet , Peter L. Bartlett

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

Machine Learning · Computer Science 2025-12-01 Zhenghan Fang , Mateo Díaz , Sam Buchanan , Jeremias Sulam

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Computer Vision and Pattern Recognition · Computer Science 2024-08-26 Defang Chen , Zhenyu Zhou , Jian-Ping Mei , Chunhua Shen , Chun Chen , Can Wang

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…

Machine Learning · Statistics 2025-08-12 Xuefeng Gao , Lingjiong Zhu

Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…

Machine Learning · Computer Science 2025-06-04 Emile Pierret , Bruno Galerne

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

Machine Learning · Statistics 2026-03-13 Lea Kunkel

Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…

Numerical Analysis · Mathematics 2025-06-17 Yuehaw Khoo , Mathias Oster , Yifan Peng

Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based…

Machine Learning · Computer Science 2025-08-25 Yi Zhang , Zhenyu Liao , Jingfeng Wu , Difan Zou

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…

Numerical Analysis · Mathematics 2026-01-28 Pengjun Wang , Zezhong Zhang , Minglei Yang , Feng Bao , Yanzhao Cao , Guannan Zhang

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…

Machine Learning · Computer Science 2026-04-14 Mudit Gaur , Prashant Trivedi , Sasidhar Kunapuli , Amrit Singh Bedi , Vaneet Aggarwal

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

Machine Learning · Statistics 2026-05-29 Jingda Wu , Changxiao Cai

We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…

Machine Learning · Computer Science 2024-10-10 Akhil Premkumar

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…

Machine Learning · Computer Science 2023-10-04 Guoqiang Zhang , Niwa Kenta , W. Bastiaan Kleijn

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…

Machine Learning · Statistics 2023-03-06 Kazusato Oko , Shunta Akiyama , Taiji Suzuki

Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…

Machine Learning · Statistics 2026-02-27 Pascal Jutras-Dube , Jiaru Zhang , Ziran Wang , Ruqi Zhang

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

Computer Vision and Pattern Recognition · Computer Science 2026-03-19 Liangyu Yuan , Ruoyu Wang , Tong Zhao , Dingwen Fu , Mingkun Lei , Beier Zhu , Chi Zhang

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…

Machine Learning · Statistics 2025-08-25 Nishant Jain , Tong Zhang