Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality Article Swipe
Zhihan Huang
,
Yuting Wei
,
Yuxin Chen
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.18784
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.18784
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional to the ambient data dimension, resulting in overly conservative theory that fails to explain its practical efficiency. This has motivated the recent work Li and Yan (2024a) to investigate how the DDPM can achieve sampling speed-ups through automatic exploitation of intrinsic low dimensionality of data. We strengthen this line of work by demonstrating, in some sense, optimal adaptivity to unknown low dimensionality. For a broad class of data distributions with intrinsic dimension $k$, we prove that the iteration complexity of the DDPM scales nearly linearly with $k$, which is optimal when using KL divergence to measure distributional discrepancy. Notably, our work is closely aligned with the independent concurrent work Potaptchik et al. (2024) -- posted two weeks prior to ours -- in establishing nearly linear-$k$ convergence guarantees for the DDPM.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2410.18784
- https://arxiv.org/pdf/2410.18784
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404342063
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4404342063Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2410.18784Digital Object Identifier
- Title
-
Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalityWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-10-24Full publication date if available
- Authors
-
Zhihan Huang, Yuting Wei, Yuxin ChenList of authors in order
- Landing page
-
https://arxiv.org/abs/2410.18784Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2410.18784Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2410.18784Direct OA link when available
- Concepts
-
Probabilistic logic, Curse of dimensionality, Diffusion, Dimensionality reduction, Computer science, Artificial intelligence, Mathematical optimization, Statistical physics, Mathematics, Physics, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4404342063 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2410.18784 |
| ids.doi | https://doi.org/10.48550/arxiv.2410.18784 |
| ids.openalex | https://openalex.org/W4404342063 |
| fwci | |
| type | preprint |
| title | Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10320 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.7142000198364258 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1702 |
| topics[0].subfield.display_name | Artificial Intelligence |
| topics[0].display_name | Neural Networks and Applications |
| topics[1].id | https://openalex.org/T12603 |
| topics[1].field.id | https://openalex.org/fields/31 |
| topics[1].field.display_name | Physics and Astronomy |
| topics[1].score | 0.713699996471405 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/3106 |
| topics[1].subfield.display_name | Nuclear and High Energy Physics |
| topics[1].display_name | NMR spectroscopy and applications |
| topics[2].id | https://openalex.org/T12100 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.7044000029563904 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1703 |
| topics[2].subfield.display_name | Computational Theory and Mathematics |
| topics[2].display_name | Advanced Mathematical Modeling in Engineering |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C49937458 |
| concepts[0].level | 2 |
| concepts[0].score | 0.8009811639785767 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q2599292 |
| concepts[0].display_name | Probabilistic logic |
| concepts[1].id | https://openalex.org/C111030470 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6964603662490845 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q1430460 |
| concepts[1].display_name | Curse of dimensionality |
| concepts[2].id | https://openalex.org/C69357855 |
| concepts[2].level | 2 |
| concepts[2].score | 0.5725103616714478 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q163214 |
| concepts[2].display_name | Diffusion |
| concepts[3].id | https://openalex.org/C70518039 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5354623198509216 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q16000077 |
| concepts[3].display_name | Dimensionality reduction |
| concepts[4].id | https://openalex.org/C41008148 |
| concepts[4].level | 0 |
| concepts[4].score | 0.47856953740119934 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[4].display_name | Computer science |
| concepts[5].id | https://openalex.org/C154945302 |
| concepts[5].level | 1 |
| concepts[5].score | 0.3910279870033264 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[5].display_name | Artificial intelligence |
| concepts[6].id | https://openalex.org/C126255220 |
| concepts[6].level | 1 |
| concepts[6].score | 0.3559029996395111 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[6].display_name | Mathematical optimization |
| concepts[7].id | https://openalex.org/C121864883 |
| concepts[7].level | 1 |
| concepts[7].score | 0.3333005905151367 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q677916 |
| concepts[7].display_name | Statistical physics |
| concepts[8].id | https://openalex.org/C33923547 |
| concepts[8].level | 0 |
| concepts[8].score | 0.32537150382995605 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[8].display_name | Mathematics |
| concepts[9].id | https://openalex.org/C121332964 |
| concepts[9].level | 0 |
| concepts[9].score | 0.14511334896087646 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[9].display_name | Physics |
| concepts[10].id | https://openalex.org/C97355855 |
| concepts[10].level | 1 |
| concepts[10].score | 0.0 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q11473 |
| concepts[10].display_name | Thermodynamics |
| keywords[0].id | https://openalex.org/keywords/probabilistic-logic |
| keywords[0].score | 0.8009811639785767 |
| keywords[0].display_name | Probabilistic logic |
| keywords[1].id | https://openalex.org/keywords/curse-of-dimensionality |
| keywords[1].score | 0.6964603662490845 |
| keywords[1].display_name | Curse of dimensionality |
| keywords[2].id | https://openalex.org/keywords/diffusion |
| keywords[2].score | 0.5725103616714478 |
| keywords[2].display_name | Diffusion |
| keywords[3].id | https://openalex.org/keywords/dimensionality-reduction |
| keywords[3].score | 0.5354623198509216 |
| keywords[3].display_name | Dimensionality reduction |
| keywords[4].id | https://openalex.org/keywords/computer-science |
| keywords[4].score | 0.47856953740119934 |
| keywords[4].display_name | Computer science |
| keywords[5].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[5].score | 0.3910279870033264 |
| keywords[5].display_name | Artificial intelligence |
| keywords[6].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[6].score | 0.3559029996395111 |
| keywords[6].display_name | Mathematical optimization |
| keywords[7].id | https://openalex.org/keywords/statistical-physics |
| keywords[7].score | 0.3333005905151367 |
| keywords[7].display_name | Statistical physics |
| keywords[8].id | https://openalex.org/keywords/mathematics |
| keywords[8].score | 0.32537150382995605 |
| keywords[8].display_name | Mathematics |
| keywords[9].id | https://openalex.org/keywords/physics |
| keywords[9].score | 0.14511334896087646 |
| keywords[9].display_name | Physics |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2410.18784 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2410.18784 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2410.18784 |
| locations[1].id | doi:10.48550/arxiv.2410.18784 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | cc-by |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2410.18784 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5115593884 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Zhihan Huang |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Huang, Zhihan |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5005015806 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-1488-4647 |
| authorships[1].author.display_name | Yuting Wei |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Wei, Yuting |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5100416081 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-2645-0881 |
| authorships[2].author.display_name | Yuxin Chen |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Chen, Yuxin |
| authorships[2].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2410.18784 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T10320 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.7142000198364258 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1702 |
| primary_topic.subfield.display_name | Artificial Intelligence |
| primary_topic.display_name | Neural Networks and Applications |
| related_works | https://openalex.org/W1995622179, https://openalex.org/W1484111231, https://openalex.org/W4391160746, https://openalex.org/W1552543208, https://openalex.org/W2074396517, https://openalex.org/W2166963679, https://openalex.org/W2187269125, https://openalex.org/W1641615907, https://openalex.org/W3089231081, https://openalex.org/W2093956241 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2410.18784 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2410.18784 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2410.18784 |
| primary_location.id | pmh:oai:arXiv.org:2410.18784 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2410.18784 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2410.18784 |
| publication_date | 2024-10-24 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 9, 96 |
| abstract_inverted_index.-- | 146, 153 |
| abstract_inverted_index.KL | 125 |
| abstract_inverted_index.Li | 56 |
| abstract_inverted_index.We | 78 |
| abstract_inverted_index.as | 8 |
| abstract_inverted_index.by | 84 |
| abstract_inverted_index.et | 143 |
| abstract_inverted_index.in | 13, 30, 39, 86, 154 |
| abstract_inverted_index.is | 121, 134 |
| abstract_inverted_index.of | 72, 76, 82, 99, 112 |
| abstract_inverted_index.to | 33, 45, 60, 91, 127, 151 |
| abstract_inverted_index.we | 106 |
| abstract_inverted_index.AI. | 15 |
| abstract_inverted_index.For | 95 |
| abstract_inverted_index.The | 0 |
| abstract_inverted_index.Yan | 58 |
| abstract_inverted_index.al. | 144 |
| abstract_inverted_index.and | 57 |
| abstract_inverted_index.can | 65 |
| abstract_inverted_index.for | 23, 160 |
| abstract_inverted_index.has | 6, 51 |
| abstract_inverted_index.how | 62 |
| abstract_inverted_index.is, | 29 |
| abstract_inverted_index.its | 47 |
| abstract_inverted_index.low | 74, 93 |
| abstract_inverted_index.our | 132 |
| abstract_inverted_index.the | 24, 26, 34, 53, 63, 109, 113, 138, 161 |
| abstract_inverted_index.two | 148 |
| abstract_inverted_index.$k$, | 105, 119 |
| abstract_inverted_index.DDPM | 64, 114 |
| abstract_inverted_index.This | 50 |
| abstract_inverted_index.been | 21 |
| abstract_inverted_index.data | 36, 100 |
| abstract_inverted_index.have | 20 |
| abstract_inverted_index.line | 81 |
| abstract_inverted_index.ours | 152 |
| abstract_inverted_index.some | 87 |
| abstract_inverted_index.that | 43, 108 |
| abstract_inverted_index.this | 80 |
| abstract_inverted_index.when | 123 |
| abstract_inverted_index.with | 102, 118, 137 |
| abstract_inverted_index.work | 55, 83, 133, 141 |
| abstract_inverted_index.DDPM, | 25 |
| abstract_inverted_index.DDPM. | 162 |
| abstract_inverted_index.While | 16 |
| abstract_inverted_index.broad | 97 |
| abstract_inverted_index.class | 98 |
| abstract_inverted_index.data. | 77 |
| abstract_inverted_index.fails | 44 |
| abstract_inverted_index.model | 4, 12 |
| abstract_inverted_index.prior | 150 |
| abstract_inverted_index.prove | 107 |
| abstract_inverted_index.sharp | 17 |
| abstract_inverted_index.using | 124 |
| abstract_inverted_index.weeks | 149 |
| abstract_inverted_index.which | 120 |
| abstract_inverted_index.(2024) | 145 |
| abstract_inverted_index.(DDPM) | 5 |
| abstract_inverted_index.nearly | 116, 156 |
| abstract_inverted_index.overly | 40 |
| abstract_inverted_index.posted | 147 |
| abstract_inverted_index.recent | 54 |
| abstract_inverted_index.scales | 115 |
| abstract_inverted_index.sense, | 88 |
| abstract_inverted_index.theory | 42 |
| abstract_inverted_index.(2024a) | 59 |
| abstract_inverted_index.achieve | 66 |
| abstract_inverted_index.aligned | 136 |
| abstract_inverted_index.ambient | 35 |
| abstract_inverted_index.closely | 135 |
| abstract_inverted_index.emerged | 7 |
| abstract_inverted_index.explain | 46 |
| abstract_inverted_index.measure | 128 |
| abstract_inverted_index.optimal | 89, 122 |
| abstract_inverted_index.through | 69 |
| abstract_inverted_index.unknown | 92 |
| abstract_inverted_index.Notably, | 131 |
| abstract_inverted_index.general, | 31 |
| abstract_inverted_index.linearly | 117 |
| abstract_inverted_index.sampling | 67 |
| abstract_inverted_index.automatic | 70 |
| abstract_inverted_index.denoising | 1 |
| abstract_inverted_index.diffusion | 2 |
| abstract_inverted_index.dimension | 104 |
| abstract_inverted_index.intrinsic | 73, 103 |
| abstract_inverted_index.iteration | 27, 110 |
| abstract_inverted_index.motivated | 52 |
| abstract_inverted_index.practical | 48 |
| abstract_inverted_index.resulting | 38 |
| abstract_inverted_index.speed-ups | 68 |
| abstract_inverted_index.Potaptchik | 142 |
| abstract_inverted_index.adaptivity | 90 |
| abstract_inverted_index.complexity | 28, 111 |
| abstract_inverted_index.concurrent | 140 |
| abstract_inverted_index.dimension, | 37 |
| abstract_inverted_index.divergence | 126 |
| abstract_inverted_index.generative | 11, 14 |
| abstract_inverted_index.guarantees | 19, 159 |
| abstract_inverted_index.linear-$k$ | 157 |
| abstract_inverted_index.mainstream | 10 |
| abstract_inverted_index.strengthen | 79 |
| abstract_inverted_index.convergence | 18, 158 |
| abstract_inverted_index.efficiency. | 49 |
| abstract_inverted_index.established | 22 |
| abstract_inverted_index.independent | 139 |
| abstract_inverted_index.investigate | 61 |
| abstract_inverted_index.conservative | 41 |
| abstract_inverted_index.discrepancy. | 130 |
| abstract_inverted_index.establishing | 155 |
| abstract_inverted_index.exploitation | 71 |
| abstract_inverted_index.proportional | 32 |
| abstract_inverted_index.distributions | 101 |
| abstract_inverted_index.probabilistic | 3 |
| abstract_inverted_index.demonstrating, | 85 |
| abstract_inverted_index.dimensionality | 75 |
| abstract_inverted_index.distributional | 129 |
| abstract_inverted_index.dimensionality. | 94 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |