Diffusion Models are Minimax Optimal Distribution Estimators
Authors: Kazusato Oko, Shunta Akiyama, Taiji Suzuki
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs. |
| Researcher Affiliation | Academia | 1Department of Mathematical Informatics, the University of Tokyo, Tokyo, Japan 2Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan. Correspondence to: Kazusato Oko <okokazusato@g.ecc.u-tokyo.ac.jp>. |
| Pseudocode | No | The paper describes mathematical derivations and theoretical concepts but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper is theoretical and does not report on empirical experiments using specific datasets. |
| Dataset Splits | No | The paper is theoretical and does not report on empirical experiments; therefore, no dataset splits are provided. |
| Hardware Specification | No | The paper focuses on theoretical analysis and does not report on empirical experiments; therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper focuses on theoretical analysis and does not report on empirical experiments; therefore, no software dependencies with version numbers are listed. |
| Experiment Setup | No | The paper focuses on theoretical analysis and does not report on empirical experiments; therefore, no experimental setup details like hyperparameters or training configurations are provided. |