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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"…

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…

Computer Vision and Pattern Recognition · Computer Science 2023-04-14 Severi Rissanen , Markus Heinonen , Arno Solin

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…

Machine Learning · Computer Science 2022-11-23 Valentin De Bortoli , Emile Mathieu , Michael Hutchinson , James Thornton , Yee Whye Teh , Arnaud Doucet

Diffusion models trained on noisy datasets often reproduce high-frequency training artifacts, significantly degrading generation quality. To address this, we propose SCoRe (Spectral Cutoff Regeneration), a training-free, generation-time…

Computer Vision and Pattern Recognition · Computer Science 2026-04-13 Yuta Matsuzaki , Seiichi Uchida , Shumpei Takezaki

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…

Machine Learning · Computer Science 2026-02-09 Adrian Baule

Recent advances in generative artificial intelligence have had a significant impact on diverse domains spanning computer vision, natural language processing, and drug discovery. This work extends the reach of generative models into physical…

Machine Learning · Computer Science 2024-10-22 Christian Jacobsen , Yilin Zhuang , Karthik Duraisamy

This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…

Machine Learning · Computer Science 2024-12-30 Jathin Korrapati , Tanish Baranwal , Rahul Shah

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Machine Learning · Statistics 2023-06-12 Aaron Lou , Stefano Ermon

Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the…

Audio and Speech Processing · Electrical Eng. & Systems 2022-07-08 Simon Welker , Julius Richter , Timo Gerkmann

Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…

Machine Learning · Statistics 2023-04-06 Valentin De Bortoli , James Thornton , Jeremy Heng , Arnaud Doucet

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in…

Machine Learning · Computer Science 2023-06-19 Pavel Avdeyev , Chenlai Shi , Yuhao Tan , Kseniia Dudnyk , Jian Zhou

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…

Machine Learning · Computer Science 2023-02-10 Sandesh Ghimire , Jinyang Liu , Armand Comas , Davin Hill , Aria Masoomi , Octavia Camps , Jennifer Dy

Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…

Optimization and Control · Mathematics 2026-05-13 Kang Liu , Enrique Zuazua

Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative…

Machine Learning · Statistics 2025-10-29 Adam Nordenhög , Akash Sharma

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean…

Machine Learning · Computer Science 2023-06-01 Ziwei Luo , Fredrik K. Gustafsson , Zheng Zhao , Jens Sjölund , Thomas B. Schön

Score-based generative models can effectively learn the distribution of data by estimating the gradient of the distribution. Due to the multi-step denoising characteristic, researchers have recently considered combining score-based…

Machine Learning · Computer Science 2024-12-17 Changyuan Zhao , Hongyang Du , Guangyuan Liu , Dusit Niyato

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…

Machine Learning · Computer Science 2021-10-15 Qinsheng Zhang , Yongxin Chen

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

Machine Learning · Computer Science 2022-10-26 Sarthak Mittal , Guillaume Lajoie , Stefan Bauer , Arash Mehrjou

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Machine Learning · Computer Science 2020-10-13 Yang Song , Stefano Ermon

Score-based generative models (SGMs) have demonstrated unparalleled sampling quality and diversity in numerous fields, such as image generation, voice synthesis, and tabular data synthesis, etc. Inspired by those outstanding results, we…

Machine Learning · Computer Science 2025-11-27 Haksoo Lim , Jaehoon Lee , Sewon Park , Minjung Kim , Noseong Park