Generation-Powered Inference for Distribution-Valued Outcomes

[2608.14542] Generation-Powered Inference for Distribution-Valued Outcomes Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2608.14542 (stat) [Submitted on 14 Aug 2026] Title: Generation-Powered Inference for Distribution-Valued Outcomes Authors: Yijiao Zhang , Hongzhe Li View a PDF of the paper titled Generation-Powered Inference for Distribution-Valued Outcomes, by Yijiao Zhang and Hongzhe Li View PDF HTML (experimental) Abstract: Modern generative models increasingly produce distribution-valued outputs, such as predicted cellular responses to genetic perturbations in single-cell genomics. While these models provide valuable auxiliary information, they are inherently imperfect, creating a need for statistical methods that leverage their predictions without relying on their correctness. We propose generation-powered inference (GPI), a general framework for improving inference on distribution-valued parameters using auxiliary generative models. Focusing on Wasserstein barycenters and related distributional functionals, we introduce a function-valued bridge representation that transforms inference in the nonlinear Wasserstein space into estimation of a mean function in a Hilbert space, enabling an augmented estimation framework analogous to prediction-powered inference. We develop a family of GPI estimators with optimal information borrowing, establish consistency, asymptotic normality, and simultaneous confidence bands, and derive valid inference for linear functionals and Wasserstein distances. Simulation studies demonstrate efficiency gains over labeled-data-only methods and robust performance under generative model misspecification. We illustrate the proposed framework using a Perturb-seq study of K562 cells, where synthetic perturbation responses generated by the State foundation model are used to improve inference for pathway-level consensus gene expression distributions associated with perturbations of the 40S ribosome module. Comments: 36 pages, 5 figures Subjects: Methodology (stat.ME) ; Machine Learning (stat.ML) Cite as: arXiv:2608.14542 [stat.ME] (or arXiv:2608.14542v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2608.14542 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yijiao Zhang [ view email ] [v1] Fri, 14 Aug 2026 17:55:48 UTC (1,694 KB) Full-text links: Access Paper: View a PDF of the paper titled Generation-Powered Inference for Distribution-Valued Outcomes, by Yijiao Zhang and Hongzhe Li View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-08 Change to browse by: 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? ) 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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