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Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM:…

Machine Learning · Computer Science 2023-05-04 Holden Lee , Jianfeng Lu , Yixin Tan

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

This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…

Statistics Theory · Mathematics 2024-06-07 Elen Vardanyan , Sona Hunanyan , Tigran Galstyan , Arshak Minasyan , Arnak Dalalyan

Score-based generative models (SGMs) need to approximate the scores $\nabla \log p_t$ of the intermediate distributions as well as the final distribution $p_T$ of the forward process. The theoretical underpinnings of the effects of these…

Machine Learning · Statistics 2022-10-18 Jakiw Pidstrigach

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function…

Machine Learning · Computer Science 2024-05-28 Connor Mooney , Zhongjian Wang , Jack Xin , Yifeng Yu

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

Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…

Machine Learning · Statistics 2025-10-24 Zijun Gao , Yan Sun , Han Su

We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstrate that, via mean-field games (MFGs), the WPO formulation…

Machine Learning · Statistics 2024-02-12 Benjamin J. Zhang , Siting Liu , Wuchen Li , Markos A. Katsoulakis , Stanley J. Osher

This paper studies the approximation and generalization abilities of score-based neural network generative models (SGMs) in estimating an unknown distribution $P_0$ from $n$ i.i.d. observations in $d$ dimensions. Assuming merely that $P_0$…

Machine Learning · Computer Science 2025-10-28 Guoji Fu , Wee Sun Lee

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…

Machine Learning · Computer Science 2023-01-23 Haksoo Lim , Minjung Kim , Sewon Park , Noseong Park

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

Machine Learning · Statistics 2024-02-26 Frank Cole , Yulong Lu

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…

Machine Learning · Computer Science 2021-02-11 Yang Song , Jascha Sohl-Dickstein , Diederik P. Kingma , Abhishek Kumar , Stefano Ermon , Ben Poole

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…

Machine Learning · Computer Science 2025-02-18 Stefano Bruno , Ying Zhang , Dong-Young Lim , Ömer Deniz Akyildiz , Sotirios Sabanis

How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…

Machine Learning · Statistics 2023-11-17 Li Kevin Wenliang , Ben Moran

Score-based generative models (SGMs) are a popular family of deep generative models that achieve leading image generation quality. Early studies extend SGMs to tackle class-conditional generation by coupling an unconditional SGM with the…

Computer Vision and Pattern Recognition · Computer Science 2024-02-08 Paul Kuo-Ming Huang , Si-An Chen , Hsuan-Tien Lin

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…

Machine Learning · Statistics 2026-05-15 Tiziano Fassina , Gabriel Cardoso , Sylvan Le Corff , Thomas Romary

We adopt a Gamma and Malliavin Calculi point of view in order to generalize Score-based diffusion Generative Models (SGMs) to an infinite-dimensional abstract Hilbertian setting. Particularly, we define the forward noising process using…

Probability · Mathematics 2025-10-06 Giacomo Greco

Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary time-dependent stochasticity parameter or a probability flow ODE, corresponding…

Machine Learning · Computer Science 2025-07-31 Bernardo P. Schaeffer , Ricardo M. S. Rosa , Glauco Valle

Score-based generative models (SGMs) have revolutionized the field of generative modeling, achieving unprecedented success in generating realistic and diverse content. Despite empirical advances, the theoretical basis for why optimizing the…

Machine Learning · Computer Science 2024-08-30 Gen Li , Yuling Yan

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…

Machine Learning · Statistics 2022-03-28 Tim Dockhorn , Arash Vahdat , Karsten Kreis