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In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated…

Machine Learning · Computer Science 2024-03-26 Tangjun Wang , Chenglong Bao , Zuoqiang Shi

In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…

Machine Learning · Computer Science 2023-06-06 Etrit Haxholli , Marco Lorenzi

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…

Machine Learning · Computer Science 2026-05-21 Wei Huang , Andi Han , Mingyuan Bai , Huanjian Zhou , Qixin Zhang , Taiji Suzuki , Kenji Fukumizu

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Machine Learning · Statistics 2026-03-17 Xiang Li , Zebang Shen , Ya-Ping Hsieh , Niao He

With the growing interest in foundation models for brain signals, graph-based pretraining has emerged as a promising paradigm for learning transferable representations from connectome data. However, existing contrastive and masked…

Machine Learning · Computer Science 2026-03-10 Xinxu Wei , Rong Zhou , Lifang He , Yu Zhang

Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models…

Machine Learning · Statistics 2025-08-11 Esha Saha , Giang Tran

It is well known that training a denoising score-based diffusion models requires tens of thousands of epochs and a substantial number of image data to train the model. In this paper, we propose to increase the efficiency in training…

Computer Vision and Pattern Recognition · Computer Science 2024-04-11 Andrew S. Na , William Gao , Justin W. L. Wan

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Image and Video Processing · Electrical Eng. & Systems 2025-05-20 Chicago Y. Park , Shirin Shoushtari , Hongyu An , Ulugbek S. Kamilov

Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…

Computer Vision and Pattern Recognition · Computer Science 2024-03-13 Anwaar Ulhaq , Naveed Akhtar

Diffusion-based inpainting is a powerful tool for the reconstruction of images from sparse data. Its quality strongly depends on the choice of known data. Optimising their spatial location -- the inpainting mask -- is challenging. A…

Image and Video Processing · Electrical Eng. & Systems 2022-05-17 Tobias Alt , Pascal Peter , Joachim Weickert

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Image and Video Processing · Electrical Eng. & Systems 2025-05-22 Yuanhao Wang , Shirin Shoushtari , Ulugbek S. Kamilov

Score-based diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which…

Machine Learning · Computer Science 2024-12-25 Davide Scassola , Sebastiano Saccani , Ginevra Carbone , Luca Bortolussi

We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…

Machine Learning · Computer Science 2026-05-26 Yanbo Xu , Yu Wu , Sungjae Park , Zhizhuo Zhou , Shubham Tulsiani

We develop a neural network architecture which, trained in an unsupervised manner as a denoising diffusion model, simultaneously learns to both generate and segment images. Learning is driven entirely by the denoising diffusion objective,…

Computer Vision and Pattern Recognition · Computer Science 2023-12-12 Xin Yuan , Michael Maire

Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…

Machine Learning · Computer Science 2024-09-04 Solveig Klepper

Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…

Machine Learning · Computer Science 2025-10-17 Yutian Zhao , Chao Du , Xiaosen Zheng , Tianyu Pang , Min Lin

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Machine Learning · Computer Science 2023-05-02 Lequan Lin , Zhengkun Li , Ruikun Li , Xuliang Li , Junbin Gao

Machine learning (ML) is used for many earth science applications; however, traditional ML methods trained with squared errors often create blurry forecasts. Diffusion models are an emerging generative ML technique with the ability to…

Machine Learning · Computer Science 2025-12-22 Randy J. Chase , Katherine Haynes , Lander Ver Hoef , Imme Ebert-Uphoff

Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…

Computer Vision and Pattern Recognition · Computer Science 2024-08-21 Md Manjurul Ahsan , Shivakumar Raman , Yingtao Liu , Zahed Siddique

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift…

Machine Learning · Statistics 2026-02-19 Nail B. Khelifa , Richard E. Turner , Ramji Venkataramanan
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