{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:Z4TQHAW4J3WBR6P2YPNCP2J3B3","short_pith_number":"pith:Z4TQHAW4","schema_version":"1.0","canonical_sha256":"cf270382dc4eec18f9fac3da27e93b0ee82b99567eb1f163b4059b14cee9abd9","source":{"kind":"arxiv","id":"2303.18242","version":2},"attestation_state":"computed","paper":{"title":"$\\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Chris G. Willcocks, Sam Bond-Taylor","submitted_at":"2023-03-31T17:58:08Z","abstract_excerpt":"This paper introduces $\\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arbitrary resolution sampling. Unlike prior neural field-based infinite-dimensional models, which use point-wise functions requiring latent compression, our method employs non-local integral operators to map between Hilbert spaces, allowing spatial context aggregation. This is achieved with an efficient "},"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":"2303.18242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-31T17:58:08Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"7c8548b5c52a7ace8787e0e1c95386e6fa5f347d048121287cb5e16e63533298","abstract_canon_sha256":"b7c6e1de4f28db23b15f49a58acb6215d9f4a781bc2976fae4bf6ea709092c57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:50:49.411955Z","signature_b64":"gen/DZRM3RvPjph9jGv/stt6luEleMLyYxhfkObf002zlE20Juiwfiioi6SFmYARinMqLyOcroNaGwDLh4L4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf270382dc4eec18f9fac3da27e93b0ee82b99567eb1f163b4059b14cee9abd9","last_reissued_at":"2026-07-05T07:50:49.411596Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:50:49.411596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Chris G. Willcocks, Sam Bond-Taylor","submitted_at":"2023-03-31T17:58:08Z","abstract_excerpt":"This paper introduces $\\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arbitrary resolution sampling. Unlike prior neural field-based infinite-dimensional models, which use point-wise functions requiring latent compression, our method employs non-local integral operators to map between Hilbert spaces, allowing spatial context aggregation. This is achieved with an efficient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.18242","kind":"arxiv","version":2},"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/2303.18242/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":"2303.18242","created_at":"2026-07-05T07:50:49.411661+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.18242v2","created_at":"2026-07-05T07:50:49.411661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.18242","created_at":"2026-07-05T07:50:49.411661+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4TQHAW4J3WB","created_at":"2026-07-05T07:50:49.411661+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4TQHAW4J3WBR6P2","created_at":"2026-07-05T07:50:49.411661+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4TQHAW4","created_at":"2026-07-05T07:50:49.411661+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02971","citing_title":"Scale-Adaptive Generative Flows for Multiscale Scientific Data","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3","json":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3.json","graph_json":"https://pith.science/api/pith-number/Z4TQHAW4J3WBR6P2YPNCP2J3B3/graph.json","events_json":"https://pith.science/api/pith-number/Z4TQHAW4J3WBR6P2YPNCP2J3B3/events.json","paper":"https://pith.science/paper/Z4TQHAW4"},"agent_actions":{"view_html":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3","download_json":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3.json","view_paper":"https://pith.science/paper/Z4TQHAW4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.18242&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4TQHAW4J3WBR6P2YPNCP2J3B3/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4TQHAW4J3WBR6P2YPNCP2J3B3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3/action/storage_attestation","attest_author":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3/action/author_attestation","sign_citation":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3/action/citation_signature","submit_replication":"https://pith.science/pith/Z4TQHAW4J3WBR6P2YPNCP2J3B3/action/replication_record"}},"created_at":"2026-07-05T07:50:49.411661+00:00","updated_at":"2026-07-05T07:50:49.411661+00:00"}