{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OAP63WLUM5K675ATLS2T5KIR6V","short_pith_number":"pith:OAP63WLU","schema_version":"1.0","canonical_sha256":"701fedd9746755eff4135cb53ea911f55bbb0941541a2f0be9b8083f6211730b","source":{"kind":"arxiv","id":"2402.05933","version":1},"attestation_state":"computed","paper":{"title":"Time Series Diffusion in the Frequency Domain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jan Stanczuk, Jonathan Crabb\\'e, Mihaela van der Schaar, Nicolas Huynh","submitted_at":"2024-02-08T18:59:05Z","abstract_excerpt":"Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brown"},"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":"2402.05933","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-08T18:59:05Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"949cff9c0952b5505aa11d80c0d8c0a5ed78ad261fdff25873cd1332ba2ebef7","abstract_canon_sha256":"8f145109aac55633c4fddde8690c3520757db104c35ae6ac051471f0a1c9ff77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:43:05.453419Z","signature_b64":"S2uLIcRYrrpb7ognGsOJJ8ixJDpxNlpQtviTxn4nEY3gUb6gdYxZiB+CVesA27I6HIIkUD4v+I/vf/CaHA9vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"701fedd9746755eff4135cb53ea911f55bbb0941541a2f0be9b8083f6211730b","last_reissued_at":"2026-07-05T07:43:05.452934Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:43:05.452934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time Series Diffusion in the Frequency Domain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jan Stanczuk, Jonathan Crabb\\'e, Mihaela van der Schaar, Nicolas Huynh","submitted_at":"2024-02-08T18:59:05Z","abstract_excerpt":"Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.05933","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/2402.05933/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":"2402.05933","created_at":"2026-07-05T07:43:05.452988+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.05933v1","created_at":"2026-07-05T07:43:05.452988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.05933","created_at":"2026-07-05T07:43:05.452988+00:00"},{"alias_kind":"pith_short_12","alias_value":"OAP63WLUM5K6","created_at":"2026-07-05T07:43:05.452988+00:00"},{"alias_kind":"pith_short_16","alias_value":"OAP63WLUM5K675AT","created_at":"2026-07-05T07:43:05.452988+00:00"},{"alias_kind":"pith_short_8","alias_value":"OAP63WLU","created_at":"2026-07-05T07:43:05.452988+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.02177","citing_title":"Low-Pass Flow Matching","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V","json":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V.json","graph_json":"https://pith.science/api/pith-number/OAP63WLUM5K675ATLS2T5KIR6V/graph.json","events_json":"https://pith.science/api/pith-number/OAP63WLUM5K675ATLS2T5KIR6V/events.json","paper":"https://pith.science/paper/OAP63WLU"},"agent_actions":{"view_html":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V","download_json":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V.json","view_paper":"https://pith.science/paper/OAP63WLU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.05933&json=true","fetch_graph":"https://pith.science/api/pith-number/OAP63WLUM5K675ATLS2T5KIR6V/graph.json","fetch_events":"https://pith.science/api/pith-number/OAP63WLUM5K675ATLS2T5KIR6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V/action/storage_attestation","attest_author":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V/action/author_attestation","sign_citation":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V/action/citation_signature","submit_replication":"https://pith.science/pith/OAP63WLUM5K675ATLS2T5KIR6V/action/replication_record"}},"created_at":"2026-07-05T07:43:05.452988+00:00","updated_at":"2026-07-05T07:43:05.452988+00:00"}