{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GGWSAIGBGVXMX4WGGWPUD4IG5Q","short_pith_number":"pith:GGWSAIGB","canonical_record":{"source":{"id":"2102.09672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-18T23:44:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"4e2dc29951e3f3625c1d250081314238ec51d711b56de8887f75705726de5415","abstract_canon_sha256":"084e01d0615c400d02aaa5f09cea919e3d7f0df92b7095fff0a7e29e81394683"},"schema_version":"1.0"},"canonical_sha256":"31ad2020c1356ecbf2c6359f41f106ec3e6b985a5ee4f2c8ce30a67f3b5d4022","source":{"kind":"arxiv","id":"2102.09672","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.09672","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"2102.09672v1","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.09672","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"GGWSAIGBGVXM","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"GGWSAIGBGVXMX4WG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"GGWSAIGB","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GGWSAIGBGVXMX4WGGWPUD4IG5Q","target":"record","payload":{"canonical_record":{"source":{"id":"2102.09672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-18T23:44:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"4e2dc29951e3f3625c1d250081314238ec51d711b56de8887f75705726de5415","abstract_canon_sha256":"084e01d0615c400d02aaa5f09cea919e3d7f0df92b7095fff0a7e29e81394683"},"schema_version":"1.0"},"canonical_sha256":"31ad2020c1356ecbf2c6359f41f106ec3e6b985a5ee4f2c8ce30a67f3b5d4022","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:46.862127Z","signature_b64":"T3AiMkyfJlu2Y+Z6nuaJsKXIVnVE/X+ORci/yO4vMG4O5S3jkdTkw6CIC1qGY0aiMDEhdTzAqlGMv14SFIyrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ad2020c1356ecbf2c6359f41f106ec3e6b985a5ee4f2c8ce30a67f3b5d4022","last_reissued_at":"2026-05-17T23:38:46.861530Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:46.861530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.09672","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LMWA5BdGx6yxzMT5Vu9q4txdl2iazcRh1om4E5l7CmVEu43/Sau+L5wgFe5Rv35DsNFu5Kyptih7LZlZlTrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:52:37.354777Z"},"content_sha256":"6d184a5bec7de80c0385669822de04658e44ab8fd5a15c59c777ad6ee151ab85","schema_version":"1.0","event_id":"sha256:6d184a5bec7de80c0385669822de04658e44ab8fd5a15c59c777ad6ee151ab85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GGWSAIGBGVXMX4WGGWPUD4IG5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Denoising Diffusion Probabilistic Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling.","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alex Nichol, Prafulla Dhariwal","submitted_at":"2021-02-18T23:44:17Z","abstract_excerpt":"Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen modifications to the noise schedule and variance parameterization do not introduce unmeasured biases in the learned distribution or sampling dynamics beyond what the reported metrics capture.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Targeted tweaks to DDPMs produce competitive likelihoods and high-quality samples, with learned reverse variances enabling 10x faster sampling and predictable scaling with compute.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2118f6fc99ebc0835cf236c045cbb67c81f02ce3cffb4d1721a9025c2de7ef3f"},"source":{"id":"2102.09672","kind":"arxiv","version":1},"verdict":{"id":"e6030429-ad94-4c1a-b774-cc0fa9ea9572","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:15:07.553096Z","strongest_claim":"We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality.","one_line_summary":"Targeted tweaks to DDPMs produce competitive likelihoods and high-quality samples, with learned reverse variances enabling 10x faster sampling and predictable scaling with compute.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen modifications to the noise schedule and variance parameterization do not introduce unmeasured biases in the learned distribution or sampling dynamics beyond what the reported metrics capture.","pith_extraction_headline":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling."},"references":{"count":17,"sample":[{"doi":"","year":null,"title":"Large Scale GAN Training for High Fidelity Natural Image Synthesis","work_id":"244e6f06-bad2-4f34-8186-ff370286427f","ref_index":1,"cited_arxiv_id":"1809.11096","is_internal_anchor":true},{"doi":"","year":2011,"title":"Very deep vaes generalize autoregressive models and can outperform them on images","work_id":"214ff54a-9ea1-46bc-94a9-8daf75f1d2b9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Gans trained by a two time-scale update rule converge to a local nash equilibrium","work_id":"ee703933-f9ee-4a48-8621-5b66c0322d6d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1902,"title":"Flow++: Improving ﬂow-based generative models with variational dequantization and architecture design","work_id":"58dad468-996a-4b27-af63-673e9a09dfe9","ref_index":4,"cited_arxiv_id":"1902.00275","is_internal_anchor":true},{"doi":"","year":2009,"title":"Kynk¨a¨anniemi, T., Karras, T., Laine, S., Lehtinen, J., and Aila, T","work_id":"57a3305f-67e0-48e5-b939-33ac062b4b60","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":17,"snapshot_sha256":"8c6f8996e9a08ce74790d6a0faa84ff44c437f9badfc692f93d43c6244e6722e","internal_anchors":3},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d76da9291b9c1eaf4f5b75f28ef3a0f2bdd14086981db0298a76c4bc840cacf5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"e6030429-ad94-4c1a-b774-cc0fa9ea9572"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b60hbZtGRuGYjyG0WYV0g+8SrsEAUrJmZB53ldUqsXpSYurDxMRP6gkOvUp8lr+4BvI6Cu0ngDT3LxuBukLZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:52:37.355361Z"},"content_sha256":"1c64e8ec66f925259b9fab97da0c975617d4ee7fa63fd2a146d80b654e3c3f21","schema_version":"1.0","event_id":"sha256:1c64e8ec66f925259b9fab97da0c975617d4ee7fa63fd2a146d80b654e3c3f21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/bundle.json","state_url":"https://pith.science/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T07:52:37Z","links":{"resolver":"https://pith.science/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q","bundle":"https://pith.science/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/bundle.json","state":"https://pith.science/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGWSAIGBGVXMX4WGGWPUD4IG5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GGWSAIGBGVXMX4WGGWPUD4IG5Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"084e01d0615c400d02aaa5f09cea919e3d7f0df92b7095fff0a7e29e81394683","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-18T23:44:17Z","title_canon_sha256":"4e2dc29951e3f3625c1d250081314238ec51d711b56de8887f75705726de5415"},"schema_version":"1.0","source":{"id":"2102.09672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.09672","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"2102.09672v1","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.09672","created_at":"2026-05-17T23:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"GGWSAIGBGVXM","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"GGWSAIGBGVXMX4WG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"GGWSAIGB","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:1c64e8ec66f925259b9fab97da0c975617d4ee7fa63fd2a146d80b654e3c3f21","target":"graph","created_at":"2026-05-17T23:38:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the chosen modifications to the noise schedule and variance parameterization do not introduce unmeasured biases in the learned distribution or sampling dynamics beyond what the reported metrics capture."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Targeted tweaks to DDPMs produce competitive likelihoods and high-quality samples, with learned reverse variances enabling 10x faster sampling and predictable scaling with compute."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling."}],"snapshot_sha256":"2118f6fc99ebc0835cf236c045cbb67c81f02ce3cffb4d1721a9025c2de7ef3f"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d76da9291b9c1eaf4f5b75f28ef3a0f2bdd14086981db0298a76c4bc840cacf5"},"paper":{"abstract_excerpt":"Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs","authors_text":"Alex Nichol, Prafulla Dhariwal","cross_cats":["cs.AI","stat.ML"],"headline":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-18T23:44:17Z","title":"Improved Denoising Diffusion Probabilistic Models"},"references":{"count":17,"internal_anchors":3,"resolved_work":17,"sample":[{"cited_arxiv_id":"1809.11096","doi":"","is_internal_anchor":true,"ref_index":1,"title":"Large Scale GAN Training for High Fidelity Natural Image Synthesis","work_id":"244e6f06-bad2-4f34-8186-ff370286427f","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Very deep vaes generalize autoregressive models and can outperform them on images","work_id":"214ff54a-9ea1-46bc-94a9-8daf75f1d2b9","year":2011},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Gans trained by a two time-scale update rule converge to a local nash equilibrium","work_id":"ee703933-f9ee-4a48-8621-5b66c0322d6d","year":2017},{"cited_arxiv_id":"1902.00275","doi":"","is_internal_anchor":true,"ref_index":4,"title":"Flow++: Improving ﬂow-based generative models with variational dequantization and architecture design","work_id":"58dad468-996a-4b27-af63-673e9a09dfe9","year":1902},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Kynk¨a¨anniemi, T., Karras, T., Laine, S., Lehtinen, J., and Aila, T","work_id":"57a3305f-67e0-48e5-b939-33ac062b4b60","year":2009}],"snapshot_sha256":"8c6f8996e9a08ce74790d6a0faa84ff44c437f9badfc692f93d43c6244e6722e"},"source":{"id":"2102.09672","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-16T19:15:07.553096Z","id":"e6030429-ad94-4c1a-b774-cc0fa9ea9572","model_set":{"reader":"grok-4.3"},"one_line_summary":"Targeted tweaks to DDPMs produce competitive likelihoods and high-quality samples, with learned reverse variances enabling 10x faster sampling and predictable scaling with compute.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Simple modifications let denoising diffusion models achieve competitive log-likelihoods while supporting much faster sampling.","strongest_claim":"We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality.","weakest_assumption":"That the chosen modifications to the noise schedule and variance parameterization do not introduce unmeasured biases in the learned distribution or sampling dynamics beyond what the reported metrics capture."}},"verdict_id":"e6030429-ad94-4c1a-b774-cc0fa9ea9572"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6d184a5bec7de80c0385669822de04658e44ab8fd5a15c59c777ad6ee151ab85","target":"record","created_at":"2026-05-17T23:38:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"084e01d0615c400d02aaa5f09cea919e3d7f0df92b7095fff0a7e29e81394683","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-18T23:44:17Z","title_canon_sha256":"4e2dc29951e3f3625c1d250081314238ec51d711b56de8887f75705726de5415"},"schema_version":"1.0","source":{"id":"2102.09672","kind":"arxiv","version":1}},"canonical_sha256":"31ad2020c1356ecbf2c6359f41f106ec3e6b985a5ee4f2c8ce30a67f3b5d4022","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ad2020c1356ecbf2c6359f41f106ec3e6b985a5ee4f2c8ce30a67f3b5d4022","first_computed_at":"2026-05-17T23:38:46.861530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:38:46.861530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T3AiMkyfJlu2Y+Z6nuaJsKXIVnVE/X+ORci/yO4vMG4O5S3jkdTkw6CIC1qGY0aiMDEhdTzAqlGMv14SFIyrDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:38:46.862127Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.09672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d184a5bec7de80c0385669822de04658e44ab8fd5a15c59c777ad6ee151ab85","sha256:1c64e8ec66f925259b9fab97da0c975617d4ee7fa63fd2a146d80b654e3c3f21"],"state_sha256":"eec9a7875e111060427c2affa7d43cc1334db0260d3ceadadaa0a9aa79e02fb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64KxGcXPoF0RcgZyTmhI5aE3xR22xrZo4nI3I4JCUOH9i2ogvs1i9/8l6u9r4PMYLSgmS1Jqj9gtV+F/G+OWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:52:37.357866Z","bundle_sha256":"5c2609f96ac94907a3c6de47f578fd90534de8ed3f4088237557dbea58fb71b8"}}