Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access

[2505.18344] Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2505.18344 (cs) [Submitted on 23 May 2025 ( v1 ), last revised 11 Apr 2026 (this version, v7)] Title: Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access Authors: Mudit Gaur , Prashant Trivedi , Sasidhar Kunapuli , Amrit Singh Bedi , Vaneet Aggarwal View a PDF of the paper titled Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access, by Mudit Gaur and 4 other authors View PDF HTML (experimental) Abstract: Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data dimension or rely on unrealistic assumptions such as access to exact empirical risk minimizers. In this work, we provide a principled analysis of score estimation, establishing a sample complexity bound of $\mathcal{O}(\epsilon^{-4})$. Our approach leverages a structured decomposition of the score estimation error into statistical, approximation, and optimization errors, enabling us to eliminate the exponential dependence on neural network parameters that arises in prior analyses. It is the first such result that achieves sample complexity bounds without assuming access to the empirical risk minimizer of score function estimation loss. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2505.18344 [cs.LG] (or arXiv:2505.18344v7 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2505.18344 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Transactions on Machine Learning Research, Apr 2026 Submission history From: Vaneet Aggarwal [ view email ] [v1] Fri, 23 May 2025 20:02:15 UTC (57 KB) [v2] Sun, 8 Jun 2025 04:22:21 UTC (57 KB) [v3] Tue, 19 Aug 2025 05:22:14 UTC (62 KB) [v4] Mon, 29 Sep 2025 01:21:38 UTC (77 KB) [v5] Sat, 4 Oct 2025 02:28:12 UTC (79 KB) [v6] Wed, 12 Nov 2025 08:39:36 UTC (78 KB) [v7] Sat, 11 Apr 2026 18:08:15 UTC (83 KB) Full-text links: Access Paper: View a PDF of the paper titled Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access, by Mudit Gaur and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2025-05 Change to browse by: cs cs.AI stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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