{"paper":{"title":"Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Huijie Zhang, Peng Wang, Qing Qu, Siyi Chen, Yi Ma, Zekai Zhang","submitted_at":"2024-09-04T04:14:02Z","abstract_excerpt":"Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood. In this work, we develop a new mathematical framework that explains how diffusion models can effectively learn low-dimensional distributions from a finite number of training samples without suffering from the curse of dimensionality. Specifically, motivated by the intrinsic low-dimensional structure of image data, we theoretically analyze a setting in which the data distribution is modeled as a mixture "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02426","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.02426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}