{"paper":{"title":"A PDE-Based Framework for Generative Modeling Beyond Classical Score-Based Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Horacio Tettamanti, Michael Herty","submitted_at":"2026-07-02T15:53:21Z","abstract_excerpt":"We introduce an alternative generative framework based on a nonlinear modification of the classical Ornstein--Uhlenbeck dynamics. The proposed dynamics admits both a microscopic description through an interacting particle system and, in the mean-field limit, a macroscopic formulation given by a nonlinear Fokker--Planck equation with a superlinear drift term. We show that, for suitable choices of the model parameters and sufficiently large initial mass, the forward dynamics exhibits condensation phenomena by proving the loss of $L^2$ regularity of the solution in finite time. Building upon this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02349","kind":"arxiv","version":1},"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/2607.02349/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"}