Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models

[2608.15103] Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2608.15103 (math) [Submitted on 15 Aug 2026] Title: Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models Authors: Tongyao Pang , Zuowei Shen , Ruitong Zhang View a PDF of the paper titled Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models, by Tongyao Pang and 2 other authors View PDF HTML (experimental) Abstract: Diffusion models learn to reverse a predefined corruption process, but sampling still requires a costly time discretization and depends on the chosen noise schedule. We study these two issues for variance-preserving diffusions with matrix-valued schedules. Our analysis transfers reverse-time discretization errors to the forward corruption law and treats two numerical schemes within a common framework. The first freezes the score and yields, through a matrix-sensitive local comparison and forward information dissipation, an ambient-dimensional step complexity with leading factor $d/\varepsilon^2$ for KL accuracy $\varepsilon^2$. The second keeps the known Gaussian drift exact and freezes the posterior mean. For data of metric-entropy dimension $k$, a forward Markov identity, an anisotropic covering estimate, and Stieltjes integration by parts give the corresponding factor $k\log k/\varepsilon^2$. In both cases, the proof identifies a local error, accumulates it through the forward evolution, and inserts the result into a common KL decomposition. The local errors further provide directional criteria for matrix schedules and an asymptotically optimal square-root adaptive grid. A high-dimensional Gaussian-mixture experiment illustrates the resulting schedule and grid improvements. Subjects: Statistics Theory (math.ST) ; Information Theory (cs.IT) Cite as: arXiv:2608.15103 [math.ST] (or arXiv:2608.15103v1 [math.ST] for this version) https://doi.org/10.48550/arXiv.2608.15103 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tongyao Pang [ view email ] [v1] Sat, 15 Aug 2026 07:58:35 UTC (270 KB) Full-text links: Access Paper: View a PDF of the paper titled Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models, by Tongyao Pang and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2026-08 Change to browse by: cs cs.IT math math.IT stat stat.TH 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? ) 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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