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Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present…

Machine Learning · Computer Science 2022-10-07 Jiaming Song , Chenlin Meng , Stefano Ermon

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Numerical Analysis · Mathematics 2025-03-25 Yvann Le Fay , Simo Särkkä , Adrien Corenflos

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

Denoising Diffusion Probabilistic Models (DDPM) have recently gained significant attention. DDPMs compose a Markovian process that begins in the data domain and gradually adds noise until reaching pure white noise. DDPMs generate…

Computer Vision and Pattern Recognition · Computer Science 2024-07-09 Shady Abu-Hussein , Raja Giryes

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned F\"{o}llmer flow, which efficiently transforms a Gaussian measure into a desired target measure at time 1. To discretize the flow, we apply…

Methodology · Statistics 2023-11-08 Zhao Ding , Yuling Jiao , Xiliang Lu , Zhijian Yang , Cheng Yuan

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…

Machine Learning · Computer Science 2025-12-16 Yansong Gao , Yu Sun

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Machine Learning · Computer Science 2025-11-18 Sepehr Maleki , Negar Pourmoazemi

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

Score-based diffusion models have achieved remarkable empirical success in generating high-quality samples from target data distributions. Among them, the Denoising Diffusion Probabilistic Model (DDPM) is one of the most widely used…

Machine Learning · Statistics 2025-12-16 Yuchen Jiao , Yuchen Zhou , Gen Li

With recent technological advances, process logs, which were traditionally deterministic in nature, are being captured from non-deterministic sources, such as uncertain sensors or machine learning models (that predict activities using…

Machine Learning · Computer Science 2025-10-28 Maximilian Matyash , Avigdor Gal , Arik Senderovich

We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…

Machine Learning · Statistics 2025-10-14 Jinyuan Chang , Zhao Ding , Yuling Jiao , Ruoxuan Li , Jerry Zhijian Yang

Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…

Machine Learning · Computer Science 2026-05-12 Samuel Hurault , Thomas Moreau , Gabriel Peyré

We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that have achieved success in a wide variety of sampling tasks. In…

Optimization and Control · Mathematics 2024-02-06 Karthik Elamvazhuthi , Darshan Gadginmath , Fabio Pasqualetti

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…

Image and Video Processing · Electrical Eng. & Systems 2022-11-01 Xutao Guo , Yanwu Yang , Chenfei Ye , Shang Lu , Yang Xiang , Ting Ma

Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…

In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…

Machine Learning · Statistics 2026-02-24 Saptarshi Roy , Alessandro Rinaldo , Purnamrita Sarkar

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

Machine Learning · Computer Science 2025-11-14 Eliot Beyler , Francis Bach

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the…

Machine Learning · Computer Science 2023-03-07 Sitan Chen , Giannis Daras , Alexandros G. Dimakis

Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…

Machine Learning · Statistics 2026-05-28 Zhengyan Wan , Yidong Ouyang , Liyan Xie , Hongyuan Zha , Fang Fang , Guang Cheng