{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AQWDKZULL5PLEBC7ZLDXKGOM4V","short_pith_number":"pith:AQWDKZUL","schema_version":"1.0","canonical_sha256":"042c35668b5f5eb2045fcac77519cce55e884d592c6fe578c774e41c0724e1ab","source":{"kind":"arxiv","id":"2504.10283","version":1},"attestation_state":"computed","paper":{"title":"$\\alpha$-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Chaoran Cheng, Ge Liu, Jiahan Li, Jiajun Fan","submitted_at":"2025-04-14T14:51:45Z","abstract_excerpt":"Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State Discrete Flow Matching (CS-DFM). Existing CS-DFM models differ significantly in their representations and geometric assumptions. This work presents a unified framework for CS-DFM models, under which the existing variants can be understood as operating on different $\\alpha$-representations of probabilities. Building upon the theory of information geometry, we "},"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":"2504.10283","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-14T14:51:45Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"6daa89b6b873c92d835f99f516c2a938bbaac167ab31bd6298e37233cf6630d1","abstract_canon_sha256":"392e56b0ab33f50140ce48de647b53b861feae0c472f8421e2992f1d0c2afb91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:50.527193Z","signature_b64":"d4v0QclqF4DdVPVDHLfAJNaPz25YCQPu5TxQFTEBr49MLvOkVoTx6nu947kGLxgu9N5H+Epf5JXYBgvr8vwkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"042c35668b5f5eb2045fcac77519cce55e884d592c6fe578c774e41c0724e1ab","last_reissued_at":"2026-07-05T10:48:50.526683Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:50.526683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\alpha$-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Chaoran Cheng, Ge Liu, Jiahan Li, Jiajun Fan","submitted_at":"2025-04-14T14:51:45Z","abstract_excerpt":"Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State Discrete Flow Matching (CS-DFM). Existing CS-DFM models differ significantly in their representations and geometric assumptions. This work presents a unified framework for CS-DFM models, under which the existing variants can be understood as operating on different $\\alpha$-representations of probabilities. Building upon the theory of information geometry, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10283","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/2504.10283/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":"2504.10283","created_at":"2026-07-05T10:48:50.526743+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.10283v1","created_at":"2026-07-05T10:48:50.526743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10283","created_at":"2026-07-05T10:48:50.526743+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQWDKZULL5PL","created_at":"2026-07-05T10:48:50.526743+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQWDKZULL5PLEBC7","created_at":"2026-07-05T10:48:50.526743+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQWDKZUL","created_at":"2026-07-05T10:48:50.526743+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.24140","citing_title":"A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2601.21831","citing_title":"Generative Modeling of Discrete Data Using Geometric Latent Subspaces","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.11748","citing_title":"LangFlow: Continuous Diffusion Rivals Discrete in Language Modeling","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15009","citing_title":"Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matching","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V","json":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V.json","graph_json":"https://pith.science/api/pith-number/AQWDKZULL5PLEBC7ZLDXKGOM4V/graph.json","events_json":"https://pith.science/api/pith-number/AQWDKZULL5PLEBC7ZLDXKGOM4V/events.json","paper":"https://pith.science/paper/AQWDKZUL"},"agent_actions":{"view_html":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V","download_json":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V.json","view_paper":"https://pith.science/paper/AQWDKZUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.10283&json=true","fetch_graph":"https://pith.science/api/pith-number/AQWDKZULL5PLEBC7ZLDXKGOM4V/graph.json","fetch_events":"https://pith.science/api/pith-number/AQWDKZULL5PLEBC7ZLDXKGOM4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V/action/storage_attestation","attest_author":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V/action/author_attestation","sign_citation":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V/action/citation_signature","submit_replication":"https://pith.science/pith/AQWDKZULL5PLEBC7ZLDXKGOM4V/action/replication_record"}},"created_at":"2026-07-05T10:48:50.526743+00:00","updated_at":"2026-07-05T10:48:50.526743+00:00"}