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We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…

Optimization and Control · Mathematics 2024-11-06 Martin Burger , Matthias J. Ehrhardt , Lorenz Kuger , Lukas Weigand

Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…

Machine Learning · Computer Science 2025-04-08 Gen Li , Changxiao Cai , Yuting Wei

The Diffusion Probabilistic Model (DPM) has recently gained popularity in the field of computer vision, thanks to its image generation applications, such as Imagen, Latent Diffusion Models, and Stable Diffusion, which have demonstrated…

Image and Video Processing · Electrical Eng. & Systems 2023-12-27 Junde Wu , Wei Ji , Huazhu Fu , Min Xu , Yueming Jin , Yanwu Xu

Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some…

Machine Learning · Statistics 2025-12-18 Hugo Lavenant , Giacomo Zanella

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…

Optimization and Control · Mathematics 2021-03-02 Rahul Ranjan Jha , Anamika Dubey

Efficiently solving large-scale optimal power flow (OPF) problems is challenging due to the high dimensionality and interconnectivity of modern power systems. Decomposition methods offer a promising solution via partitioning large problems…

Optimization and Control · Mathematics 2025-12-30 Mohannad Alkhraijah , Devon Sigler , Daniel K. Molzahn

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce…

Computer Vision and Pattern Recognition · Computer Science 2026-05-08 Tao Liu , Hao Yan , Mengting Chen , Taihang Hu , Zhengrong Yue , Zihao Pan , Jinsong Lan , Xiaoyong Zhu , Ming-Ming Cheng , Bo Zheng , Yaxing Wang

Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures,…

Machine Learning · Computer Science 2025-08-06 Quan Xiao , Hui Yuan , A F M Saif , Gaowen Liu , Ramana Kompella , Mengdi Wang , Tianyi Chen

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation…

Machine Learning · Computer Science 2024-12-09 Sirui Xie , Zhisheng Xiao , Diederik P Kingma , Tingbo Hou , Ying Nian Wu , Kevin Patrick Murphy , Tim Salimans , Ben Poole , Ruiqi Gao

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

Diffusion models have achieved remarkable progress in the field of image generation due to their outstanding capabilities. However, these models require substantial computing resources because of the multi-step denoising process during…

Computer Vision and Pattern Recognition · Computer Science 2024-10-23 Haowei Zhu , Dehua Tang , Ji Liu , Mingjie Lu , Jintu Zheng , Jinzhang Peng , Dong Li , Yu Wang , Fan Jiang , Lu Tian , Spandan Tiwari , Ashish Sirasao , Jun-Hai Yong , Bin Wang , Emad Barsoum

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires…

Machine Learning · Computer Science 2023-02-28 Qinsheng Zhang , Yongxin Chen

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

Recently, rectified flow (RF)-based models have achieved state-of-the-art performance in many areas for both the multi-step and one-step generation. However, only a few theoretical works analyze the discretization complexity of RF-based…

Machine Learning · Computer Science 2025-08-13 Ruofeng Yang , Zhaoyu Zhu , Bo Jiang , Cheng Chen , Shuai Li

Image super-resolution is a fundamentally ill-posed problem because multiple valid high-resolution images exist for one low-resolution image. Super-resolution methods based on diffusion probabilistic models can deal with the ill-posed…

Computer Vision and Pattern Recognition · Computer Science 2024-04-17 Yutao Yuan , Chun Yuan

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 Probabilistic Models (DPMs) are a well-established class of diffusion models for unconditional image generation, while SGMSE+ is a well-established conditional diffusion model for speech enhancement. One of the downsides of…

Audio and Speech Processing · Electrical Eng. & Systems 2026-03-11 Bunlong Lay , Timo Gerkmann

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant…

Computer Vision and Pattern Recognition · Computer Science 2026-05-27 Dengyang Jiang , Xin Jin , Dongyang Liu , Zanyi Wang , Mingzhe Zheng , Ruoyi Du , Xiangpeng Yang , Qilong Wu , Zhen Li , Peng Gao , Harry Yang , Steven Hoi

Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the…

Machine Learning · Computer Science 2022-02-14 Daniel Watson , William Chan , Jonathan Ho , Mohammad Norouzi

Without using explicit reward, direct preference optimization (DPO) employs paired human preference data to fine-tune generative models, a method that has garnered considerable attention in large language models (LLMs). However, exploration…

Computer Vision and Pattern Recognition · Computer Science 2025-03-25 Yunhong Lu , Qichao Wang , Hengyuan Cao , Xierui Wang , Xiaoyin Xu , Min Zhang