A Probabilistic Formulation of Offset Noise in Diffusion Models

[2412.03134] A Probabilistic Formulation of Offset Noise in Diffusion Models Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2412.03134 (stat) [Submitted on 4 Dec 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: A Probabilistic Formulation of Offset Noise in Diffusion Models Authors: Takuro Kutsuna View a PDF of the paper titled A Probabilistic Formulation of Offset Noise in Diffusion Models, by Takuro Kutsuna View PDF HTML (experimental) Abstract: Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations observed in practical large-scale diffusion models. Offset noise has been proposed as an empirical solution to this issue, yet its theoretical basis remains insufficiently explored. In this paper, we propose a novel diffusion model that naturally incorporates additional noise within a rigorous probabilistic framework. Our approach modifies both the forward and reverse diffusion processes, enabling inputs to be diffused into Gaussian distributions with arbitrary mean structures. We derive a loss function based on the evidence lower bound and show that the resulting objective is structurally analogous to that of offset noise, with time-dependent coefficients. Experiments on controlled synthetic datasets demonstrate that the proposed model mitigates brightness-related limitations and achieves improved performance over conventional methods, particularly in high-dimensional settings. Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:2412.03134 [stat.ML] (or arXiv:2412.03134v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2412.03134 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Takuro Kutsuna [ view email ] [v1] Wed, 4 Dec 2024 08:57:03 UTC (1,359 KB) [v2] Thu, 9 Apr 2026 08:12:49 UTC (466 KB) Full-text links: Access Paper: View a PDF of the paper titled A Probabilistic Formulation of Offset Noise in Diffusion Models, by Takuro Kutsuna View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2024-12 Change to browse by: cs cs.LG stat 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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