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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

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

Machine Learning · Computer Science 2026-02-27 Siddharth Rout , Eldad Haber , Stephane Gaudreault

Accelerated diffusion models hold the potential to significantly enhance the efficiency of standard diffusion processes. Theoretically, these models have been shown to achieve faster convergence rates than the standard $\mathcal…

Machine Learning · Computer Science 2025-03-28 Yuchen Liang , Peizhong Ju , Yingbin Liang , Ness Shroff

Recent advances in generative artificial intelligence have enabled the creation of high-quality synthetic data that closely mimics real-world data. This paper explores the adaptation of the Stable Diffusion 2.0 model for generating…

Machine Learning · Computer Science 2024-05-07 Eugenio Lomurno , Matteo D'Oria , Matteo Matteucci

As Diffusion Models have shown promising performance, a lot of efforts have been made to improve the controllability of Diffusion Models. However, how to train Diffusion Models to have the disentangled latent spaces and how to naturally…

Computer Vision and Pattern Recognition · Computer Science 2025-07-02 Wonwoong Cho , Hareesh Ravi , Midhun Harikumar , Vinh Khuc , Krishna Kumar Singh , Jingwan Lu , David I. Inouye , Ajinkya Kale

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Machine Learning · Computer Science 2021-10-01 Chin-Wei Huang , Jae Hyun Lim , Aaron Courville

Score-based models, trained with denoising score matching, are remarkably effective in generating high dimensional data. However, the high variance of their training objective hinders optimisation. We attempt to reduce it with a control…

Machine Learning · Computer Science 2024-08-23 Paul Jeha , Will Grathwohl , Michael Riis Andersen , Carl Henrik Ek , Jes Frellsen

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

Machine Learning · Computer Science 2023-08-21 Francisco Vargas , Will Grathwohl , Arnaud Doucet

We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method for fine-tuning diffusion models to maximize differentiable reward functions, such as scores from human preference models. We first show that it is possible to…

Computer Vision and Pattern Recognition · Computer Science 2024-06-24 Kevin Clark , Paul Vicol , Kevin Swersky , David J Fleet

Diffusion models have achieved remarkable success in text-to-image generation. However, their practical applications are hindered by the misalignment between generated images and corresponding text prompts. To tackle this issue,…

Computer Vision and Pattern Recognition · Computer Science 2025-03-28 Zijing Hu , Fengda Zhang , Long Chen , Kun Kuang , Jiahui Li , Kaifeng Gao , Jun Xiao , Xin Wang , Wenwu Zhu

Diffusion models have demonstrated great potential in generating high-quality content for images, natural language, protein domains, etc. However, how to perform user-preferred targeted generation via diffusion models with only black-box…

Machine Learning · Statistics 2024-06-11 Yueming Lyu , Kim Yong Tan , Yew Soon Ong , Ivor W. Tsang

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple…

Machine Learning · Computer Science 2026-05-26 Ziheng Cheng , Yixiao Huang , Hanlin Zhu , Haoran Geng , Somayeh Sojoudi , Jitendra Malik , Pieter Abbeel , Xin Guo

We propose Speech Enhancement based on Drifting Models (DriftSE), a novel generative framework that formulates denoising as an equilibrium problem. Rather than relying on iterative sampling, DriftSE natively achieves one-step inference by…

Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…

Statistics Theory · Mathematics 2026-01-13 Yifeng Yu , Lu Yu

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…

The assumption that training and testing samples are generated from the same distribution does not always hold for real-world machine-learning applications. The procedure of tackling this discrepancy between the training (source) and…

Machine Learning · Computer Science 2018-12-05 Debasmit Das , C. S. George Lee

Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion…

Machine Learning · Computer Science 2026-01-22 Raphaël Razafindralambo , Rémy Sun , Frédéric Precioso , Damien Garreau , Pierre-Alexandre Mattei

The rapid advancement of generative models, such as Stable Diffusion, raises a key question: how can synthetic data from these models enhance predictive modeling? While they can generate vast amounts of datasets, only a subset meaningfully…

Machine Learning · Statistics 2025-05-09 Jialong Jiang , Wenkang Hu , Jian Huang , Yuling Jiao , Xu Liu

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

Machine Learning · Computer Science 2025-09-03 Andrea Montanari

Diffusion-based generative models demonstrate state-of-the-art performance across various image synthesis tasks, yet their tendency to replicate and amplify dataset biases remains poorly understood. Although previous research has viewed…

Machine Learning · Computer Science 2025-12-24 Nathan Roos , Ekaterina Iakovleva , Ani Gjergji , Vito Paolo Pastore , Enzo Tartaglione