This is a non-exhaustive list of papers. If your paper should be included, please email [email protected].
Position [BibTex]
[Mar 2025] Generalization of Diffusion Models: Principles, Theory, and Implications (SIAM News 2025)
[BibTex]
@article{zhang2025generalization,
title={Generalization of diffusion models: Principles, theory, and implications},
author={Zhang, Huijie and Wang, Peng and Chen, Siyi and Zhang, Zekai and Qu, Qing},
journal={SIAM News},
year={2025}
}Memorization to Generalization [BibTex]
[Jun 2023] Diffusion Probabilistic Models Generalize when They Fail to Memorize (ICMLW 2023)
[BibTex]
@inproceedings{
yoon2023diffusion,
title={Diffusion Probabilistic Models Generalize when They Fail to Memorize},
author={TaeHo Yoon and Joo Young Choi and Sehyun Kwon and Ernest K. Ryu},
booktitle={ICML 2023 Workshop on Structured Probabilistic Inference {\&} Generative Modeling},
year={2023},
url={https://openreview.net/forum?id=shciCbSk9h}
}[Oct 2023] Generalization in Diffusion Models Arises from Geometry-Adaptive Harmonic Representations (ICLR 2024)
[BibTex]
@inproceedings{
kadkhodaie2024generalization,
title={Generalization in diffusion models arises from geometry-adaptive harmonic representations},
author={Zahra Kadkhodaie and Florentin Guth and Eero P Simoncelli and St{\'e}phane Mallat},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=ANvmVS2Yr0}
}[Oct 2023] The Emergence of Reproducibility and Generalizability in Diffusion Models (ICML 2024)
[BibTex]
@inproceedings{
zhang2024emergence,
author={Huijie Zhang and Jinfan Zhou and Yifu Lu and Minzhe Guo and Peng Wang and Liyue Shen and Qing Qu},
title={The Emergence of Reproducibility and Consistency in Diffusion Models},
year={2024},
cdate={1704067200000},
url={https://openreview.net/forum?id=HsliOqZkc0},
booktitle={ICML},
crossref={conf/icml/2024}
}[Nov 2024] Dynamical Regimes of Diffusion Models (Nature Communications 2024)
[BibTex]
@article{biroli2024dynamical,
title={Dynamical regimes of diffusion models},
author={Biroli, Giulio and Bonnaire, Tony and De Bortoli, Valentin and M{\'e}zard, Marc},
journal={Nature Communications},
volume={15},
number={1},
pages={9957},
year={2024},
publisher={Nature Publishing Group UK London}
}[Jan 2025] Memorization and Regularization in Generative Diffusion Models
[BibTex]
@article{baptista2025memorization,
title={Memorization and regularization in generative diffusion models},
author={Baptista, Ricardo and Dasgupta, Agnimitra and Kovachki, Nikola B and Oberai, Assad and Stuart, Andrew M},
journal={arXiv preprint arXiv:2501.15785},
year={2025}
}[Feb 2025] Memorization and Generalization in Generative Diffusion under the Manifold Hypothesis (JSTAT 2025)
[BibTex]
@article{achilli2025memorization,
title={Memorization and generalization in generative diffusion under the manifold hypothesis},
author={Achilli, Beatrice and Ambrogioni, Luca and Lucibello, Carlo and M{\'e}zard, Marc and Ventura, Enrico},
journal={Journal of Statistical Mechanics: Theory and Experiment},
volume={2025},
number={7},
pages={073401},
year={2025},
publisher={IOP Publishing}
}[Feb 2025] Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion (ICML 2025)
[BibTex]
@inproceedings{
shah2025does,
title={Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion},
author={Kulin Shah and Alkis Kalavasis and Adam Klivans and Giannis Daras},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=GGPM0z3dhU}
}[May 2025] Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces
[BibTex]
@article{lyu2025resolving,
title={Resolving memorization in empirical diffusion model for manifold data in high-dimensional spaces},
author={Lyu, Yang and Nguyen, Tan Minh and Qian, Yuchun and Tong, Xin T},
journal={arXiv preprint arXiv:2505.02508},
year={2025}
}[May 2025] Understanding Generalization in Diffusion Distillation via Probability Flow Distance
[BibTex]
@article{zhang2025understanding,
title={Understanding generalization in diffusion models via probability flow distance},
author={Zhang, Huijie and Huang, Zijian and Chen, Siyi and Zhou, Jinfan and Zhang, Zekai and Wang, Peng and Qu, Qing},
journal={arXiv preprint arXiv:2505.20123},
year={2025}
}[May 2025] Memorization to Generalization: Emergence of Diffusion Models from Associative Memory (NeurIPSW 2024)
[BibTex]
@inproceedings{
pham2024memorization,
title={Memorization to Generalization: The Emergence of Diffusion Models from Associative Memory},
author={Bao Pham and Gabriel Raya and Matteo Negri and Mohammed J Zaki and Luca Ambrogioni and Dmitry Krotov},
booktitle={NeurIPS 2024 Workshop on Scientific Methods for Understanding Deep Learning},
year={2024},
url={https://openreview.net/forum?id=zVMMaVy2BY}
}[Jun 2025] Rethinking Memorization–Generalization Trade-Off in Generative Models (ICMLW 2025)
[BibTex]
@inproceedings{
chae2025rethinking,
title={Rethinking Memorization{\textendash}Generalization Trade-Off in Generative Models},
author={Jiseok Chae and Kyuwon Kim and Donghwan Kim},
booktitle={High-dimensional Learning Dynamics 2025},
year={2025},
url={https://openreview.net/forum?id=JIMZsqE8bA}
}[Jun 2025] When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets (ICML 2025)
[BibTex]
@inproceedings{
zeno2025when,
title={When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets},
author={Chen Zeno and Hila Manor and Greg Ongie and Nir Weinberger and Tomer Michaeli and Daniel Soudry},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=WD2CKUrxmx}
}[Jun 2025] Generative Modeling of Weights: Generalization or Memorization? (CVPR 2026)
[BibTex]
@article{zeng2025generative,
title={Generative Modeling of Weights: Generalization or Memorization?},
author={Zeng, Boya and Yin, Yida and Xu, Zhiqiu and Liu, Zhuang},
journal={arXiv preprint arXiv:2506.07998},
year={2025}
}[Jun 2025] On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity (NeurIPS 2025)
[BibTex]
@inproceedings{bertrand2025closed,
title={On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity},
author={Bertrand, Quentin and Gagneux, Anne and Massias, Mathurin and Emonet, R{\'e}mi},
booktitle={NeurIPS 2025},
year={2025}
url={https://openreview.net/forum?id=kVz9uvqUna}
}[Aug 2025] On the Edge of Memorization in Diffusion Models (NeurIPS 2025)
[BibTex]
@inproceedings{
buchanan2025on,
title={On the Edge of Memorization in Diffusion Models},
author={Sam Buchanan and Druv Pai and Yi Ma and Valentin De Bortoli},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=rWW5wdECl8}
}[Sep 2025] A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective (NeurIPS 2025)
[BibTex]
@inproceedings{
shi2025a,
title={A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective},
author={Lianghe Shi and Meng Wu and Huijie Zhang and Zekai Zhang and Molei Tao and Qing Qu},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=6xCcjYa97j}
}[Oct 2025] The Generation Phases of Flow Matching: a Denoising Perspective
[BibTex]
@article{gagneux2025generation,
title={The Generation Phases of Flow Matching: a Denoising Perspective},
author={Gagneux, Anne and Martin, S{\'e}gol{\`e}ne and Gribonval, R{\'e}mi and Massias, Mathurin},
journal={arXiv preprint arXiv:2510.24830},
year={2025}
}[Nov 2025] Provable Separations between Memorization and Generalization in Diffusion Models (ICLR 2026)
[BibTex]
@inproceedings{
ye2026provable,
title={Provable Separations between Memorization and Generalization in Diffusion Models},
author={Zeqi Ye and Qijie Zhu and Molei Tao and Minshuo Chen},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=42gfTZzyvV}
}[Jan 2026] Statistical Physics of Generative Diffusion (PhD Thesis, Bocconi 2026)
[BibTex]
@article{achilli2026statistical,
title={Statistical Physics of Generative Diffusion},
author={Achilli, Beatrice and others},
year={2026},
publisher={Universit{\`a} Bocconi}
}[Jan 2026] Smoothing the Score Function for Generalization in Diffusion Models: An Optimization-based Explanation Framework (CVPR 2026)
[BibTex]
@article{zhou2026smoothing,
title={Smoothing the Score Function for Generalization in Diffusion Models: An Optimization-based Explanation Framework},
author={Zhou, Xinyu and Zhang, Jiawei and Wright, Stephen J},
journal={arXiv preprint arXiv:2601.19285},
year={2026}
}[Feb 2026] Two Calm Ends and the Wild Middle: A Geometric Picture of Memorization in Diffusion Models
[BibTex]
@article{dodson2026two,
title={Two Calm Ends and the Wild Middle: A Geometric Picture of Memorization in Diffusion Models},
author={Dodson, Nick and Gao, Xinyu and Wang, Qingsong and Wang, Yusu and Wan, Zhengchao},
journal={arXiv preprint arXiv:2602.17846},
year={2026}
}[Mar 2026] Manifold Generalization Provably Proceeds Memorization in Diffusion Models (ICLRW 2026)
[BibTex]
@inproceedings{
shen2026manifold,
title={Manifold Generalization Provably Proceeds Memorization in Diffusion Models},
author={Zebang Shen and Ya-Ping Hsieh and Niao He},
booktitle={ICLR 2026 Workshop on Geometry-grounded Representation Learning and Generative Modeling},
year={2026},
url={https://openreview.net/forum?id=O9StcESgB5}
}[Mar 2026] Biased Generalization in Diffusion Models
[BibTex]
@article{garnier2026biased,
title={Biased Generalization in Diffusion Models},
author={Garnier-Brun, Jerome and Biggio, Luca and Beltrame, Davide and M{\'e}zard, Marc and Saglietti, Luca},
journal={arXiv preprint arXiv:2603.03469},
year={2026}
}[Mar 2026] Generalization and Memorization in Rectified Flow
[BibTex]
@article{rao2026generalization,
title={Generalization and Memorization in Rectified Flow},
author={Rao, Mingxing and Moyer, Daniel},
journal={arXiv preprint arXiv:2603.13421},
year={2026}
}Empirical Observation [BibTex]
[May 2023] On the Generalization of Diffusion Model
[BibTex]
@article{
yi2023generalization,
title={On the generalization of diffusion model},
author={Yi, Mingyang and Sun, Jiacheng and Li, Zhenguo},
journal={arXiv preprint arXiv:2305.14712},
year={2023}
}[Jun 2024] Understanding Hallucinations in Diffusion Models through Mode Interpolation (NeurIPS 2024)
[BibTex]
@inproceedings{
aithal2024understanding,
title={Understanding Hallucinations in Diffusion Models through Mode Interpolation},
author={Sumukh K Aithal and Pratyush Maini and Zachary Chase Lipton and J Zico Kolter},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=aNTnHBkw4T}
}[Oct 2024] On Inductive Biases That Enable Generalization of Diffusion Transformers (NeurIPS 2025)
[BibTex]
@inproceedings{
an2025on,
title={On Inductive Biases That Enable Generalization in Diffusion Transformers},
author={Jie An and De Wang and Pengsheng Guo and Jiebo Luo and Alex Schwing},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=lE2cD7C9fk}
}Low-dimensional Structure [BibTex]
[Feb 2023] Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data (ICML 2023)
[BibTex]
@inproceedings{chen2023score,
title={Score approximation, estimation and distribution recovery of diffusion models on low-dimensional data},
author={Chen, Minshuo and Huang, Kaixuan and Zhao, Tuo and Wang, Mengdi},
booktitle={International Conference on Machine Learning},
pages={4672--4712},
year={2023},
organization={PMLR}
}[Sep 2024] Diffusion Models Learn Low-Dimensional Distributions via Subspace Clustering
[BibTex]
@inproceedings{wang2025diffusion,
title={Diffusion models learn low-dimensional distributions via subspace clustering},
author={Wang, Peng and Zhang, Huijie and Zhang, Zekai and Chen, Siyi and Ma, Yi and Qu, Qing},
booktitle={2025 IEEE 10th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
pages={211--215},
year={2025},
organization={IEEE}
}[Oct 2024] Shallow Diffusion Networks Provably Learn Hidden Low-Dimensional Structure (ICLR 2025)
[BibTex]
@inproceedings{
boffi2025shallow,
title={Shallow diffusion networks provably learn hidden low-dimensional structure},
author={Nicholas Matthew Boffi and Arthur Jacot and Stephen Tu and Ingvar Ziemann},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=KlxK4ncqWZ}
}[Nov 2024] Denoising Diffusion Probabilistic Models Are Optimally Adaptive to Unknown Low Dimensionality (MOR 2026)
[BibTex]
@article{huang2026denoising,
title={Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality},
author={Huang, Zhihan and Wei, Yuting and Chen, Yuxin},
journal={Mathematics of Operations Research},
year={2026},
publisher={INFORMS}
}[Dec 2024] Few-Shot Diffusion Models Escape the Curse of Dimensionality (NeurIPS 2024)
[BibTex]
@inproceedings{
yang2024fewshot,
title={Few-Shot Diffusion Models Escape the Curse of Dimensionality},
author={Ruofeng Yang and Bo Jiang and Cheng Chen and Ruinan Jin and Baoxiang Wang and Shuai Li},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=JrraNaaZm5}
}[Jan 2025] Low-Dimensional Adaptation of Diffusion Models: Convergence in Total Variation (COLT 2025)
[BibTex]
@InProceedings{pmlr-v291-liang25a,
title = {Low-dimensional adaptation of diffusion models: Convergence in total variation (extended abstract)},
author = {Liang, Jiadong and Huang, Zhihan and Chen, Yuxin},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
pages = {3723--3729},
year = {2025},
editor = {Haghtalab, Nika and Moitra, Ankur},
volume = {291},
series = {Proceedings of Machine Learning Research},
month = {30 Jun--04 Jul},
publisher = {PMLR},
}[Apr 2025] Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures
[BibTex]
@article{li2025dimension,
title={Dimension-free convergence of diffusion models for approximate gaussian mixtures},
author={Li, Gen and Cai, Changxiao and Wei, Yuting},
journal={arXiv preprint arXiv:2504.05300},
year={2025}
}[May 2025] Localized Diffusion Models
[BibTex]
@article{gottwald2025localized,
title={Localized Diffusion Models},
author={Gottwald, Georg A and Liu, Shuigen and Marzouk, Youssef and Reich, Sebastian and Tong, Xin T},
journal={arXiv preprint arXiv:2505.04417},
year={2025}
}[Jun 2025] On Convolutions, Intrinsic Dimension, and Diffusion Models (TMLR 2025)
[BibTex]
@article{
leung2025on,
title={On Convolutions, Intrinsic Dimension, and Diffusion Models},
author={Kin Kwan Leung and Rasa Hosseinzadeh and Gabriel Loaiza-Ganem},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2025},
url={https://openreview.net/forum?id=xSzBf1te4s},
note={Expert Certification}
}[Oct 2025] Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptive (NeurIPS 2025)
[BibTex]
@inproceedings{
farghly2025diffusion,
title={Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptive},
author={Tyler Farghly and Peter Potaptchik and Samuel Howard and George Deligiannidis and Jakiw Pidstrigach},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=4JihzQXNJn}
}[Jan 2026] Multi-Subspace Multi-Modal Modeling for Diffusion Models: Estimation, Convergence and Mixture of Experts (ICLR 2026)
[BibTex]
@inproceedings{
yang2026multisubspace,
title={Multi-Subspace Multi-Modal Modeling for Diffusion Models: Estimation, Convergence and Mixture of Experts},
author={Ruofeng Yang and Yongcan Li and Bo Jiang and Cheng Chen and Shuai Li},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=MPWIM6rxxU}
}[Feb 2026] Adaptation to Intrinsic Dependence in Diffusion Language Models
[BibTex]
@article{zhao2026adaptation,
title={Adaptation to Intrinsic Dependence in Diffusion Language Models},
author={Zhao, Yunxiao and Cai, Changxiao},
journal={arXiv preprint arXiv:2602.20126},
year={2026}
}[Mar 2026] Generalization Properties of Score-Matching Diffusion Models for Intrinsically Low-Dimensional Data
[BibTex]
@article{chakraborty2026generalization,
title={Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data},
author={Chakraborty, Saptarshi and Berthet, Quentin and Bartlett, Peter L},
journal={arXiv preprint arXiv:2603.03700},
year={2026}
}Representation Learning [BibTex]
[Feb 2025] Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling (NeurIPS 2025)
[BibTex]
@inproceedings{
li2025understanding,
title={Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling},
author={Xiao Li and Zekai Zhang and Xiang Li and Siyi Chen and Zhihui Zhu and Peng Wang and Qing Qu},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=BE6QmLdJqY}
}[Dec 2025] Generalization of Diffusion Models Arises with a Balanced Representation Space (ICLR 2026)
[BibTex]
@inproceedings{
zhang2026generalization,
title={Generalization of Diffusion Models Arises with a Balanced Representation Space},
author={Zekai Zhang and Xiao Li and Xiang Li and Lianghe Shi and Meng Wu and Molei Tao and Qing Qu},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=57THeGgNAN}
}Analytical Solution [BibTex]
[Oct 2023] Closed-Form Diffusion Models (TMLR 2025)
[BibTex]
@article{
scarvelis2025closedform,
title={Closed-Form Diffusion Models},
author={Christopher Scarvelis and Haitz S{\'a}ez de Oc{\'a}riz Borde and Justin Solomon},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2025},
url={https://openreview.net/forum?id=JkMifr17wc},
note={}
}[Oct 2024] Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structure (NeurIPS 2024)
[BibTex]
@inproceedings{
li2024understanding,
title={Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structure},
author={Xiang Li and Yixiang Dai and Qing Qu},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=Sk2duBGvrK}
}[Nov 2024] Towards a Mechanistic Explanation of Diffusion Model Generalization (ICML 2025)
[BibTex]
@inproceedings{
niedoba2025towards,
title={Towards a Mechanistic Explanation of Diffusion Model Generalization},
author={Matthew Niedoba and Berend Zwartsenberg and Kevin Patrick Murphy and Frank Wood},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=Hrp6jRIKdX}
}[Dec 2024] The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications (TMLR 2024)
[BibTex]
@article{
wang2024the,
title={The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications},
author={Binxu Wang and John Vastola},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2024},
url={https://openreview.net/forum?id=I0uknSHM2j},
note={}
}[Dec 2024] An Analytic Theory of Creativity in Convolutional Diffusion Models (ICML 2025)
[BibTex]
@inproceedings{
kamb2025an,
title={An analytic theory of creativity in convolutional diffusion models},
author={Mason Kamb and Surya Ganguli},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=ilpL2qACla}
}[Feb 2025] On the Interpolation Effect of Score Smoothing in Diffusion Models (ICLR 2026)
[BibTex]
@inproceedings{
chen2026on,
title={On the Interpolation Effect of Score Smoothing in Diffusion Models},
author={Zhengdao Chen},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=O33LAUliUF}
}[Apr 2025] Generalization through Variance: How Noise Shapes Inductive Biases in Diffusion Models (ICLR 2025)
[BibTex]
@inproceedings{
vastola2025generalization,
title={Generalization through variance: how noise shapes inductive biases in diffusion models},
author={John Vastola},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=7lUdo8Vuqa}
}[Jun 2025] On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity (NeurIPS 2025)
[BibTex]
@inproceedings{
bertrand2025on,
title={On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity},
author={Quentin Bertrand and Anne Gagneux and Mathurin Massias and R{\'e}mi Emonet},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=kVz9uvqUna}
}[Sep 2025] Locality in Image Diffusion Models Emerges from Data Statistics (NeurIPS 2025)
[BibTex]
@inproceedings{
lukoianov2025locality,
title={Locality in Image Diffusion Models Emerges from Data Statistics},
author={Artem Lukoianov and Chenyang Yuan and Justin Solomon and Vincent Sitzmann},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=skunuOdavO}
}[Oct 2025] Selective Underfitting in Diffusion Models
[BibTex]
@article{
song2025selective,
title={Selective Underfitting in Diffusion Models},
author={Song, Kiwhan and Kim, Jaeyeon and Chen, Sitan and Du, Yilun and Kakade, Sham and Sitzmann, Vincent},
journal={arXiv preprint arXiv:2510.01378},
year={2025}
}Distribution Learning Theory [BibTex]
[Mar 2023] Diffusion Models are Minimax Optimal Distribution Estimators (ICML 2023)
[BibTex]
@inproceedings{oko2023diffusion,
title={Diffusion models are minimax optimal distribution estimators},
author={Oko, Kazusato and Akiyama, Shunta and Suzuki, Taiji},
booktitle={International Conference on Machine Learning},
pages={26517--26582},
year={2023},
organization={PMLR}
}[May 2023] High-dimensional Asymptotics of Denoising Autoencoders (NeurIPS 2023)
[BibTex]
@inproceedings{
cui2023highdimensional,
title={High-dimensional Asymptotics of Denoising Autoencoders},
author={Hugo Cui and Lenka Zdeborova},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=wbbTqsiKzl}
}[Jul 2023] Learning Mixtures of Gaussians Using the DDPM Objective (NeurIPS 2023)
[BibTex]
@inproceedings{
shah2023learning,
title={Learning Mixtures of Gaussians Using the {DDPM} Objective},
author={Kulin Shah and Sitan Chen and Adam Klivans},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=aig7sgdRfI}
}[Nov 2023] On the Generalization Properties of Diffusion Models (NeurIPS 2023)
[BibTex]
@inproceedings{
li2023on,
title={On the Generalization Properties of Diffusion Models},
author={Puheng Li and Zhong Li and Huishuai Zhang and Jiang Bian},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=hCUG1MCFk5}
}[Feb 2024] Score-based Generative Models Break the Curse of Dimensionality in Learning a Family of Sub-Gaussian Probability Distributions (ICLR 2024)
[BibTex]
@inproceedings{
cole2024scorebased,
title={Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian distributions},
author={Frank Cole and Yulong Lu},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=wG12xUSqrI}
}[Feb 2024] Optimal Score Estimation via Empirical Bayes Smoothing (COLT 2024)
[BibTex]
@InProceedings{pmlr-v247-wibisono24a,
title = {Optimal score estimation via empirical Bayes smoothing},
author = {Wibisono, Andre and Wu, Yihong and Yang, Kaylee Yingxi},
booktitle = {Proceedings of Thirty Seventh Conference on Learning Theory},
pages = {4958--4991},
year = {2024},
editor = {Agrawal, Shipra and Roth, Aaron},
volume = {247},
series = {Proceedings of Machine Learning Research},
month = {30 Jun--03 Jul},
publisher = {PMLR},
}[Apr 2024] Learning Mixtures of Gaussians Using Diffusion Models (COLT 2025)
[BibTex]
@InProceedings{pmlr-v291-gatmiry25b,
title = {Learning Mixtures of Gaussians Using Diffusion Models},
author = {Gatmiry, Khashayar and Kelner, Jonathan and Lee, Holden},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
pages = {2403--2456},
year = {2025},
editor = {Haghtalab, Nika and Moitra, Ankur},
volume = {291},
series = {Proceedings of Machine Learning Research},
month = {30 Jun--04 Jul},
publisher = {PMLR},
}[Aug 2024] A Sharp Convergence Theory for the Probability Flow ODEs of Diffusion Models
[BibTex]
@article{li2024sharp,
title={A sharp convergence theory for the probability flow odes of diffusion models},
author={Li, Gen and Wei, Yuting and Chi, Yuejie and Chen, Yuxin},
journal={arXiv preprint arXiv:2408.02320},
year={2024}
}[Feb 2025] Generalization Error Bound for Denoising Score Matching under Relaxed Manifold Assumption (COLT 2025)
[BibTex]
@InProceedings{pmlr-v291-yakovlev25a,
title = {Generalization error bound for denoising score matching under relaxed manifold assumption},
author = {Yakovlev, Konstantin and Puchkin, Nikita},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
pages = {5824--5891},
year = {2025},
editor = {Haghtalab, Nika and Moitra, Ankur},
volume = {291},
series = {Proceedings of Machine Learning Research},
month = {30 Jun--04 Jul},
publisher = {PMLR},
}[Mar 2025] Minimax Optimality of the Probability Flow ODE for Diffusion Models
[BibTex]
@article{cai2025minimax,
title={Minimax optimality of the probability flow ode for diffusion models},
author={Cai, Changxiao and Li, Gen},
journal={arXiv preprint arXiv:2503.09583},
year={2025}
}[Oct 2025] Optimal Estimation of a Factorizable Density using Diffusion Models with ReLU Neural Networks
[BibTex]
@article{fan2025optimal,
title={Optimal estimation of a factorizable density using diffusion models with ReLU neural networks},
author={Fan, Jianqing and Gu, Yihong and Li, Ximing},
journal={arXiv preprint arXiv:2510.03994},
year={2025}
}[Mar 2026] A Theory of Learning Data Statistics in Diffusion Models, from Easy to Hard
[BibTex]
@article{bardone2026theory,
title={A theory of learning data statistics in diffusion models, from easy to hard},
author={Bardone, Lorenzo and Merger, Claudia and Goldt, Sebastian},
journal={arXiv preprint arXiv:2603.12901},
year={2026}
}Learning Dynamics [BibTex]
[Jan 2024] Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization (ICLR 2024)
[BibTex]
@inproceedings{
han2024neural,
title={Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization},
author={Yinbin Han and Meisam Razaviyayn and Renyuan Xu},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=h8GeqOxtd4}
}[Jun 2024] Evaluating the Design Space of Diffusion-Based Generative Models (NeurIPS 2024)
[BibTex]
@inproceedings{
wang2024evaluating,
title={Evaluating the design space of diffusion-based generative models},
author={Yuqing Wang and Ye He and Molei Tao},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=9CMOrofB75}
}[Jan 2025] A solvable model of learning generative diffusion: theory and insights (NeurIPS 2025)
[BibTex]
@inproceedings{
cui2025a,
title={A solvable model of learning generative diffusion: theory and insights},
author={Hugo Cui and Cengiz Pehlevan and Yue M. Lu},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=5b5wZg6Zeo}
}[Feb 2025] Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization (COLT 2025)
[BibTex]
@InProceedings{pmlr-v291-wu25a,
title = {Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization},
author = {Wu, Yu-Han and Marion, Pierre and Biau, G\'erard and Boyer, Claire},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
pages = {5718--5756},
year = {2025},
editor = {Haghtalab, Nika and Moitra, Ankur},
volume = {291},
series = {Proceedings of Machine Learning Research},
month = {30 Jun--04 Jul},
publisher = {PMLR},
}[Feb 2025] Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves (AISTATS 2026)
[BibTex]
@inproceedings{
george2026denoising,
title={Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves},
author={Anand Jerry George and Rodrigo Veiga and Nicolas Macris},
booktitle={The 29th International Conference on Artificial Intelligence and Statistics},
year={2026},
url={https://openreview.net/forum?id=ZnplHm2uRt}
}[Mar 2025] An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models (NeurIPS 2025)
[BibTex]
@inproceedings{
wang2025an,
title={An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models},
author={Binxu Wang and Cengiz Pehlevan},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=SDhOClkyqC}
}[May 2025] Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models
[BibTex]
@article{favero2025bigger,
title={Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models},
author={Favero, Alessandro and Sclocchi, Antonio and Wyart, Matthieu},
journal={arXiv preprint arXiv:2505.16959},
year={2025}
}[May 2025] Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training (NeurIPS 2025)
[BibTex]
@inproceedings{
bonnaire2025why,
title={Why Diffusion Models Don{\textquoteright}t Memorize: The Role of Implicit Dynamical Regularization in Training},
author={Tony Bonnaire and Rapha{\"e}l Urfin and Giulio Biroli and Marc Mezard},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=BSZqpqgqM0}
}[Jul 2025] Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis (ICLR 2026)
[BibTex]
@inproceedings{
farghly2026implicit,
title={Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis},
author={Tyler Farghly and Patrick Rebeschini and George Deligiannidis and Arnaud Doucet},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=3lSqgESdPu}
}[Nov 2025] Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussian (ICLR 2026)
[BibTex]
@inproceedings{
zhang2026convergence,
title={Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussian},
author={Yiran Zhang and Weihang Xu and Mo Zhou and Maryam Fazel and Simon Shaolei Du},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=VDIH6L8ANo}
}[BibTex]
@article{
he2026diffusion,
title={Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold},
author={He, Ye and Qiu, Yitong and Tao, Molei},
journal={arXiv preprint arXiv:2602.06021},
year={2026}
}Compositional Ability [BibTex]
[Oct 2023] Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task (NeurIPS 2023)
[BibTex]
@inproceedings{
okawa2023compositional,
title={Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task},
author={Maya Okawa and Ekdeep Singh Lubana and Robert P. Dick and Hidenori Tanaka},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=frVo9MzRuU}
}[Feb 2025] Mechanisms of Projective Composition of Diffusion Models (ICML 2025)
[BibTex]
@inproceedings{
bradley2025mechanisms,
title={Mechanisms of Projective Composition of Diffusion Models},
author={Arwen Bradley and Preetum Nakkiran and David Berthelot and James Thornton and Joshua M. Susskind},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=QV0PcBbfTd}
}[Feb 2025] How Compositional Generalization and Creativity Improve as Diffusion Models are Trained (ICML 2025)
[BibTex]
@inproceedings{
favero2025how,
title={How Compositional Generalization and Creativity Improve as Diffusion Models are Trained},
author={Alessandro Favero and Antonio Sclocchi and Francesco Cagnetta and Pascal Frossard and Matthieu Wyart},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=1OUEnfusEd}
}[Oct 2025] Seeds of Structure: Patch PCA Reveals Universal Compositional Cues in Diffusion Models (NeurIPS 2025)
[BibTex]
@inproceedings{
wang2025seeds,
title={Seeds of Structure: Patch {PCA} Reveals Universal Compositional Cues in Diffusion Models},
author={Qingsong Wang and Zhengchao Wan and Mikhail Belkin and Yusu Wang},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=EgH5WYB6my}
}Sparse Autoencoder [BibTex]
[Apr 2025] Emergence and Evolution of Interpretable Concepts in Diffusion Models (NeurIPS 2025)
[BibTex]
@inproceedings{
tinaz2025emergence,
title={Emergence and Evolution of Interpretable Concepts in Diffusion Models},
author={Berk Tinaz and Zalan Fabian and Mahdi Soltanolkotabi},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=C7LxkebvVW}
}Memorization [BibTex]
[Dec 2022] Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models (CVPR 2023)
[BibTex]
@inproceedings{somepalli2023diffusion,
title={Diffusion art or digital forgery? investigating data replication in diffusion models},
author={Somepalli, Gowthami and Singla, Vasu and Goldblum, Micah and Geiping, Jonas and Goldstein, Tom},
booktitle={Proceedings of the IEEE/CVF conference on computer vision and pattern recognition},
pages={6048--6058},
year={2023}
}[Jan 2023] Extracting Training Data from Diffusion Models (USENIX Security 2023)
[BibTex]
@inproceedings{carlini2023extracting,
title={Extracting training data from diffusion models},
author={Carlini, Nicolas and Hayes, Jamie and Nasr, Milad and Jagielski, Matthew and Sehwag, Vikash and Tramer, Florian and Balle, Borja and Ippolito, Daphne and Wallace, Eric},
booktitle={32nd USENIX security symposium (USENIX Security 23)},
pages={5253--5270},
year={2023}
}[May 2023] Understanding and Mitigating Copying in Diffusion Models (NeurIPS 2023)
[BibTex]
@inproceedings{
somepalli2023understanding,
title={Understanding and Mitigating Copying in Diffusion Models},
author={Gowthami Somepalli and Vasu Singla and Micah Goldblum and Jonas Geiping and Tom Goldstein},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=HtMXRGbUMt}
}[Oct 2023] Detecting, Explaining, and Mitigating Memorization in Diffusion Models (ICLR 2024)
[BibTex]
@inproceedings{
wen2024detecting,
title={Detecting, Explaining, and Mitigating Memorization in Diffusion Models},
author={Yuxin Wen and Yuchen Liu and Chen Chen and Lingjuan Lyu},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=84n3UwkH7b}
}[Oct 2023] On Memorization in Diffusion Models (TMLR 2025)
[BibTex]
@article{
gu2025on,
title={On Memorization in Diffusion Models},
author={Xiangming Gu and Chao Du and Tianyu Pang and Chongxuan Li and Min Lin and Ye Wang},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2025},
url={https://openreview.net/forum?id=D3DBqvSDbj},
note={}
}[Oct 2024] A Geometric Framework for Understanding Memorization in Generative Models (ICLR 2025)
[BibTex]
@inproceedings{
ross2025a,
title={A Geometric Framework for Understanding Memorization in Generative Models},
author={Brendan Leigh Ross and Hamidreza Kamkari and Tongzi Wu and Rasa Hosseinzadeh and Zhaoyan Liu and George Stein and Jesse C. Cresswell and Gabriel Loaiza-Ganem},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=aZ1gNJu8wO}
}[Oct 2024] Losing Dimensions: Geometric Memorization in Generative Diffusion
[BibTex]
@article{achilli2024losing,
title={Losing dimensions: Geometric memorization in generative diffusion},
author={Achilli, Beatrice and Ventura, Enrico and Silvestri, Gianluigi and Pham, Bao and Raya, Gabriel and Krotov, Dmitry and Lucibello, Carlo and Ambrogioni, Luca},
journal={arXiv preprint arXiv:2410.08727},
year={2024}
}[Jan 2026] Memorization Control in Diffusion Models from Denoising-centric Perspective
[BibTex]
@article{vu2026memorization,
title={Memorization Control in Diffusion Models from Denoising-centric Perspective},
author={Vu, Thuy Phuong and Do, Mai Viet Hoang and Le, Minhhuy and Hoang, Dinh-Cuong and Tan, Phan Xuan},
journal={arXiv preprint arXiv:2601.21348},
year={2026}
}