{"paper":{"title":"A note on connections between the F\\\"ollmer process and the denoising diffusion probabilistic model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Yuta Koike","submitted_at":"2026-05-18T08:31:58Z","abstract_excerpt":"The F\\\"ollmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an \"augmented\" time-compressed version of the reverse stochastic differential equation (SDE) for the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, connections between direct discretization of the F\\\"ollmer process and the DDPM sampler have not yet been fully explored. This note aims to clarify this point while surveying relevant results from exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18040","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/2605.18040/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.497917Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"12b1071eca278d3ff92aae5ed337268b8717f9fc68f903e76b4b4632e93f048d"},"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"}