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Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…

Machine Learning · Computer Science 2024-04-09 Kaiwen Zheng , Cheng Lu , Jianfei Chen , Jun Zhu

The diffusion model has shown remarkable success in computer vision, but it remains unclear whether the ODE-based probability flow or the SDE-based diffusion model is more superior and under what circumstances. Comparing the two is…

Machine Learning · Computer Science 2023-11-08 Yu Cao , Jingrun Chen , Yixin Luo , Xiang Zhou

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design…

Computer Vision and Pattern Recognition · Computer Science 2025-03-28 Jianning Pei , Han Hu , Shuyang Gu

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Machine Learning · Statistics 2024-12-12 Christopher Williams , Andrew Campbell , Arnaud Doucet , Saifuddin Syed

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can…

Machine Learning · Statistics 2022-06-28 Cheng Lu , Kaiwen Zheng , Fan Bao , Jianfei Chen , Chongxuan Li , Jun Zhu

Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that…

Computer Vision and Pattern Recognition · Computer Science 2023-10-31 Kaiwen Zheng , Cheng Lu , Jianfei Chen , Jun Zhu

One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…

Machine Learning · Computer Science 2019-06-04 Chandramouli Kamanchi , Raghuram Bharadwaj Diddigi , Prabuchandran K. J. , Shalabh Bhatnagar

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

Statistics Theory · Mathematics 2026-04-08 Arthur Stéphanovitch

We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…

Optimization and Control · Mathematics 2024-03-06 Florian Messerer , Katrin Baumgärtner , Armin Nurkanović , Moritz Diehl

Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…

Machine Learning · Computer Science 2023-04-18 Sitan Chen , Sinho Chewi , Jerry Li , Yuanzhi Li , Adil Salim , Anru R. Zhang

The denoising diffusion model has recently emerged as a powerful generative technique, capable of transforming noise into meaningful data. While theoretical convergence guarantees for diffusion models are well established when the target…

Machine Learning · Computer Science 2025-03-28 Yuchen Liang , Peizhong Ju , Yingbin Liang , Ness Shroff

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…

Machine Learning · Computer Science 2025-03-13 Chengyue Gong , Xiaoyu Li , Yingyu Liang , Jiangxuan Long , Zhenmei Shi , Zhao Song , Yu Tian

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order…

Machine Learning · Computer Science 2023-02-03 Hongrui Chen , Holden Lee , Jianfeng Lu

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

Machine Learning · Computer Science 2025-11-10 Matthew S. Zhang , Stephen Huan , Jerry Huang , Nicholas M. Boffi , Sitan Chen , Sinho Chewi

Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…

Machine Learning · Computer Science 2022-10-04 Holden Lee , Jianfeng Lu , Yixin Tan

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such…

Machine Learning · Computer Science 2026-04-14 Zhiyang Xun , Eric Price

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…

Machine Learning · Computer Science 2024-10-04 Saurabh Singh , Ian Fischer

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…