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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

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

We provide the first convergence guarantees for the Consistency Models (CMs), a newly emerging type of one-step generative models that can generate comparable samples to those generated by Diffusion Models. Our main result is that, under…

Numerical Analysis · Mathematics 2023-08-23 Junlong Lyu , Zhitang Chen , Shoubo Feng

Diffusion models have significantly advanced the fields of image, audio, and video generation, but they depend on an iterative sampling process that causes slow generation. To overcome this limitation, we propose consistency models, a new…

Machine Learning · Computer Science 2023-06-01 Yang Song , Prafulla Dhariwal , Mark Chen , Ilya Sutskever

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song…

Computer Vision and Pattern Recognition · Computer Science 2023-10-09 Simian Luo , Yiqin Tan , Longbo Huang , Jian Li , Hang Zhao

The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Linwei Dong , Ruoyu Guo , Ge Bai , Zehuan Yuan , Yawei Luo , Changqing Zou

Masked diffusion models have demonstrated competitive results on various tasks including language generation. However, due to its iterative refinement process, the inference is often bottlenecked by slow and static sampling speed. To…

Machine Learning · Computer Science 2026-03-09 Seo Hyun Kim , Sunwoo Hong , Hojung Jung , Youngrok Park , Se-Young Yun

Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into…

Machine Learning · Statistics 2024-02-13 Gen Li , Zhihan Huang , Yuting Wei

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Machine Learning · Computer Science 2024-08-06 Gen Li , Yuting Wei , Yuejie Chi , Yuxin Chen

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

Machine Learning · Computer Science 2025-11-03 Yuchen Liang , Renxiang Huang , Lifeng Lai , Ness Shroff , Yingbin Liang

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

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…

Machine Learning · Computer Science 2025-05-07 Yiding Chen , Yiyi Zhang , Owen Oertell , Wen Sun

Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model…

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…

Machine Learning · Computer Science 2025-01-23 Gen Li , Yuling Yan

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 are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then…

Statistics Theory · Mathematics 2024-09-13 Giovanni Conforti , Alain Durmus , Marta Gentiloni Silveri

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high…

Machine Learning · Computer Science 2025-12-01 Yinuo Ren , Haoxuan Chen , Yuchen Zhu , Wei Guo , Yongxin Chen , Grant M. Rotskoff , Molei Tao , Lexing Ying

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…

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

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…

Machine Learning · Statistics 2025-04-25 Peter Potaptchik , Iskander Azangulov , George Deligiannidis
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