Paper Citation Record · LEDGER

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity

As of 7 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 2 inbound Pith citation observations for arXiv:2603.20645.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2603.20645 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-15T06:41:38.834864Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T02:56:19.103411Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-02T11:46:55.999542Z

Reference resolution

32 of 32 outbound references displayed

verified exact20
verified fuzzy10
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 65f92eb8-dda2-453e-a1f7-a1842c682250 · outbound

This paper cites Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.159045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3e74b76c-2e27-4ae6-b452-2914194b428b · outbound

This paper cites Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.166262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 33a8cc1a-72ce-45e8-bed1-edfa9e8f81ab · outbound

This paper cites Generative Modeling with Denoising Auto-Encoders and Langevin Sampling.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Generative Modeling with Denoising Auto-Encoders and Langevin Sampling

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.152145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ba462cb1-f6b6-4f68-a595-1920b76225b8 · outbound

This paper cites Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-05-15T06:45:11.172799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 944bbdea-50dd-4736-b13b-72807d10768d · outbound

This paper cites Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.118893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bb847ace-cc9f-4714-ad1d-950b25a4f333 · outbound

This paper cites Convergence of denoising diffusion models under the manifold hypothesis.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Convergence of denoising diffusion models under the manifold hypothesis

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.110628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bafc8963-3f4d-40fc-b2ed-face1b9fa918 · outbound

This paper cites From optimal score matching to optimal sampling.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity From optimal score matching to optimal sampling

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.064913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ff36d339-db75-4928-b2c8-c9f558cccb0c · outbound

This paper cites Diffusion models and the manifold hypothesis: Log-domain smoothing is geometry adaptive.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Diffusion models and the manifold hypothesis: Log-domain smoothing is geometry adaptive

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.132075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6bc3b352-4cc9-4707-8b3e-2bb214c6cdfb · outbound

This paper cites Scaling Laws for Autoregressive Generative Modeling.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Scaling Laws for Autoregressive Generative Modeling

Reference 9

Resolution: metadata mismatch; local_arxiv, observed 2026-05-15T06:45:11.042001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 52e1bf52-7229-44b6-a062-4b8ddc0b2c4e · outbound

This paper cites Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.058184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cad2382a-f98a-42c9-848d-da44ecd0b28c · outbound

This paper cites Scaling Laws for Neural Language Models.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Scaling Laws for Neural Language Models

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-05-15T06:45:11.084965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dfcf8410-4881-4059-843a-f5ccdd7a8764 · outbound

This paper cites Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.145939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6e847222-aafb-46c2-b409-5fd5e9f10c2d · outbound

This paper cites Auto-Encoding Variational Bayes.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Auto-Encoding Variational Bayes

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-05-15T06:45:11.090636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5e838050-d59d-4388-a926-c6f9f29331fb · outbound

This paper cites DiffWave: A Versatile Diffusion Model for Audio Synthesis.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity DiffWave: A Versatile Diffusion Model for Audio Synthesis

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-15T13:13:37.175262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3dd1d716-60f8-468c-b76f-9d55f7d7974d · outbound

This paper cites When scores learn geometry: Rate separations under the manifold hypothesis.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity When scores learn geometry: Rate separations under the manifold hypothesis

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.072204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f34253df-297e-47f1-b97f-7313f24ddc90 · outbound

This paper cites Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-05-15T06:45:11.096634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0b8cfa53-bb40-4e31-8d5a-7a1065551321 · outbound

This paper cites Towards Understanding Text Hallucination of Diffusion Models via Local Generation Bias.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Towards Understanding Text Hallucination of Diffusion Models via Local Generation Bias

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.125487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation efd42e63-295e-4992-a2cd-9cfe16e9fc5d · outbound

This paper cites Large Language Diffusion Models.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Large Language Diffusion Models

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-05-15T06:45:11.103459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 37455b77-28a8-4cf1-a50c-7be9f3bae8a9 · outbound

This paper cites Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.050459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dcf19df0-eb49-4e40-919a-985835211cf9 · outbound

This paper cites Larry Wasserman.All of nonparametric statistics.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Larry Wasserman.All of nonparametric statistics

Reference 20

Resolution: verified exact; doi, observed 2026-05-15T06:45:10.737382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7b52c06e-e40d-4760-995d-c2372ab2f8e6 · outbound

This paper cites Generalization error bound for denoising score matching under relaxed manifold assumption.arXiv preprint arXiv:2502.13662.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Generalization error bound for denoising score matching under relaxed manifold assumption.arXiv preprint arXiv:2502.13662

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-15T06:45:11.079028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c1a0a731-a6ce-4351-84d2-030bff6d291d · outbound

This paper cites For term (♠), we use the standard identity for the squared distance to a set with positive reach [Leobacher and Steinicke, 2020] onα tK(M, τ), (♠) =− x−Π M(x, t) ht.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity For term (♠), we use the standard identity for the squared distance to a set with positive reach [Leobacher and Steinicke, 2020] onα tK(M, τ), (♠) =− x−Π M(x, t) ht

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.913805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8764a6ec-57cd-4a61-b999-78ea2e3b56db · outbound

This paper cites The approximation error ofs 1 is provided in Lemma B.1 (Appendix B.1.3).

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity The approximation error ofs 1 is provided in Lemma B.1 (Appendix B.1.3)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.911575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation aafe5495-d7f4-403c-ab78-d92d20afc67a · outbound

This paper cites Then by Lemma F.7 in Oko et al.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Then by Lemma F.7 in Oko et al

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.898005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ab3dbaa1-1d01-4c38-939f-4f131e6e6468 · outbound

This paper cites Recall that we decompose theL 2 approximation error of ¯ssmall as as ∥¯ssmall(x, t)− ∇logp t(x)∥2 L2(Pt) = Z x∈Kt(ϵ) + Z x∈RD\Kt(ϵ) ! ∥¯ssmall(x, t)− ∇logp t(x)∥2 pt(x) dx.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Recall that we decompose theL 2 approximation error of ¯ssmall as as ∥¯ssmall(x, t)− ∇logp t(x)∥2 L2(Pt) = Z x∈Kt(ϵ) + Z x∈RD\Kt(ϵ) ! ∥¯ssmall(x, t)− ∇logp t(x)∥2 pt(x) dx

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.892077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 89ecd4b6-ab17-4cb7-9b5e-8d59c820ea36 · outbound

This paper cites EX∼P data[ℓ0(X;bs)]− 1 n nX i=1 ℓ0(Xi;bs)−aR(bs) # +aE D[R(bs)] (i) =E D, ¯D.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity EX∼P data[ℓ0(X;bs)]− 1 n nX i=1 ℓ0(Xi;bs)−aR(bs) # +aE D[R(bs)] (i) =E D, ¯D

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.915754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e362fa74-04d5-4f5b-8f79-f95580b95b28 · outbound

This paper cites Moreover, by Proposition 6.1 in Niyogi et al.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Moreover, by Proposition 6.1 in Niyogi et al

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.895517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d73e28df-68db-4297-b437-53faf0d5aef4 · outbound

This paper cites Lemma D.17(Network Implementation for Tensor Product).LetC≥1.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Lemma D.17(Network Implementation for Tensor Product).LetC≥1

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.900682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d9cde3e8-6f10-4652-81e0-799409a5cea7 · outbound

This paper cites By Lemma F.1, F.2 and F.3 in Oko et al.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity By Lemma F.1, F.2 and F.3 in Oko et al

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.909122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3d2e29df-3dbd-4f1f-a7a4-88db1f5fd4f8 · outbound

This paper cites an unresolved cited work.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-15T07:00:10.905930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 99bfa85c-43fb-497d-b451-7752002f8d8e · outbound

This paper cites Notably, givenx 0 ∈U k,T k(x, x0, t) is linear inx∈R D, whileD k(x, x0, t) is quadratic in the low-dimensional representationP ⊤ k (x−α txk)∈R d.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity Notably, givenx 0 ∈U k,T k(x, x0, t) is linear inx∈R D, whileD k(x, x0, t) is quadratic in the low-dimensional representationP ⊤ k (x−α txk)∈R d

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.917790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cc481fc8-bf7e-4a75-b449-21b5d66aa732 · outbound

This paper cites The averaged Taylor polynomial can approximatef and its partial derivatives well.

Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity The averaged Taylor polynomial can approximatef and its partial derivatives well

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T07:00:10.903327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 97362f88-6785-4702-90b5-c2f3c113a4ae · inbound

Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds cites this paper.

Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity

Reference 58

Resolution: verified exact; local_arxiv, observed 2026-05-20T20:53:43.732682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c14c26df-92f3-474e-a0ac-edb6b31aec64 · inbound

Diffusion Models for Adaptive Sequential Data Generation cites this paper.

Diffusion Models for Adaptive Sequential Data Generation Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity

Reference 74

Resolution: verified exact; local_arxiv, observed 2026-07-02T11:46:56.001162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.