{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:T2SP44IVDPLHNPKHIDGGGUZVVY","short_pith_number":"pith:T2SP44IV","schema_version":"1.0","canonical_sha256":"9ea4fe71151bd676bd4740cc635335ae3cb6677fc148193fc4e5b31bea38f07c","source":{"kind":"arxiv","id":"2310.17467","version":4},"attestation_state":"computed","paper":{"title":"The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Luca Ambrogioni","submitted_at":"2023-10-26T15:15:01Z","abstract_excerpt":"Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase-transitions are always in a mean-field u"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.17467","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-26T15:15:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"879ba40f9e56185f680ed99f74202043097a458ed0f943574244f84e213e7cbe","abstract_canon_sha256":"0b1a10ab98154ca26322c5c914fa6175a8aebb164c620381dff997260a92a5bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:34:07.104428Z","signature_b64":"TEoSShrP0RXID2jmazdPD8cib/Ky/x44djBIKrCMC1M8z7usAEUvUCushcR1wc39qzIxmvQh7yPcxFl1DDJYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ea4fe71151bd676bd4740cc635335ae3cb6677fc148193fc4e5b31bea38f07c","last_reissued_at":"2026-07-05T08:34:07.103880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:34:07.103880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Luca Ambrogioni","submitted_at":"2023-10-26T15:15:01Z","abstract_excerpt":"Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase-transitions are always in a mean-field u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17467","kind":"arxiv","version":4},"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/2310.17467/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.17467","created_at":"2026-07-05T08:34:07.103943+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.17467v4","created_at":"2026-07-05T08:34:07.103943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17467","created_at":"2026-07-05T08:34:07.103943+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2SP44IVDPLH","created_at":"2026-07-05T08:34:07.103943+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2SP44IVDPLHNPKH","created_at":"2026-07-05T08:34:07.103943+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2SP44IV","created_at":"2026-07-05T08:34:07.103943+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.20299","citing_title":"Statistical Properties of Training & Generalization","ref_index":241,"is_internal_anchor":false},{"citing_arxiv_id":"2606.20299","citing_title":"Statistical Properties of Training & Generalization","ref_index":241,"is_internal_anchor":false},{"citing_arxiv_id":"2606.01645","citing_title":"Self-Regulating Annealing in Heavy-Tailed Diffusion Models","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2605.18472","citing_title":"Flowing with Confidence","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06367","citing_title":"The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Models","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY","json":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY.json","graph_json":"https://pith.science/api/pith-number/T2SP44IVDPLHNPKHIDGGGUZVVY/graph.json","events_json":"https://pith.science/api/pith-number/T2SP44IVDPLHNPKHIDGGGUZVVY/events.json","paper":"https://pith.science/paper/T2SP44IV"},"agent_actions":{"view_html":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY","download_json":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY.json","view_paper":"https://pith.science/paper/T2SP44IV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.17467&json=true","fetch_graph":"https://pith.science/api/pith-number/T2SP44IVDPLHNPKHIDGGGUZVVY/graph.json","fetch_events":"https://pith.science/api/pith-number/T2SP44IVDPLHNPKHIDGGGUZVVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY/action/storage_attestation","attest_author":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY/action/author_attestation","sign_citation":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY/action/citation_signature","submit_replication":"https://pith.science/pith/T2SP44IVDPLHNPKHIDGGGUZVVY/action/replication_record"}},"created_at":"2026-07-05T08:34:07.103943+00:00","updated_at":"2026-07-05T08:34:07.103943+00:00"}