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Paper Citation Record · LEDGER

On the Feature Learning in Diffusion Models

As of 17 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 4 inbound Pith citation observations for arXiv:2412.01021.

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

pith.paper-citation-record.v1
2412.01021 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T04:50:59.026954Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T21:50:24.513379Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T07:39:49.425945Z

Reference resolution

17 of 17 outbound references displayed

  • verified exact0
  • verified fuzzy6
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6dab1426-db7a-4abd-9fe7-bbfcbeeb492e · outbound

This paper cites 21 Published as a conference paper at ICLR 2025.

On the Feature Learning in Diffusion Models 21 Published as a conference paper at ICLR 2025

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.269005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.958322Z digest=sha256:ae123d9e128bd49100c0ad4df71835a5cedafadbba279b21d794e8c95d72bd18

Observation 4ae47193-4f33-4aec-83a3-b85fb13e77d8 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.257451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.962214Z digest=sha256:c5597e814e5dd8f7196f05335948ff40e410b132d8a77e4edff464adf74b50c1

Observation 1274cd67-700a-48e8-846d-86d1c9fe668b · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.246352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.966650Z digest=sha256:15d8d2133c9e657a505aa4ff1766681b5eefc23cf64b0d4b5bc72554d64ad06d

Observation c2ebbff6-804e-423b-a491-9223e7485d9f · outbound

This paper cites The lower bound on m = eΩ(1) is to ensure the initialization is concentrated and thus provides a lower bound on the maximum and average inner product.

On the Feature Learning in Diffusion Models The lower bound on m = eΩ(1) is to ensure the initialization is concentrated and thus provides a lower bound on the maximum and average inner product

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.235730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.971150Z digest=sha256:2e03acf0906b422639333661c7cb46d48e1f29f8ef0af9265f50f99ab526f7f5

Observation 4e920a53-d33c-48f0-ae57-d19d429d3764 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.223654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.976518Z digest=sha256:fe3e1319e09aa21d581ac30fde7c5bbef3246d517cb892423fd257ceb49bbc51

Observation b8da5d7c-caa6-4f90-8fc9-632802a08fdf · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.210824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.980756Z digest=sha256:c700bb5f9f6bc270ceae69323dc52766bd6106f13a0b8b9ac0e6bbf516a8fe28

Observation 76cf434e-6f98-4be5-9895-fe12189a8c93 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.198953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.984840Z digest=sha256:d41b446256cf491cf72b8fbad352b4b580c206f216fbb810a8a31cac01a62b6e

Observation 2d6cdb5e-9cc0-4dea-b5fe-093f596d7002 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.186088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.989422Z digest=sha256:431a28f2490cfdcc3275272c613d096b8746a51f988aa5fb44cc36b6d6278bc7

Observation c5a0128b-ac54-4550-8f01-d6db5577f4d2 · outbound

This paper cites We make the following remarks on the conditions.

On the Feature Learning in Diffusion Models We make the following remarks on the conditions

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.174503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.993930Z digest=sha256:1c09b9d2210cf86290b469c8cba7c6b96aa83c57e4c8981e8e173855fe8fc05d

Observation 70d243a5-421d-4d88-ba57-6d9e6cd6e5df · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.155261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:58.998278Z digest=sha256:7ffe5a60a1e7c5bc016bc1d05950162c32eae0d2e303e79f582298e4c8fab775

Observation 5e1b9c69-3802-46a1-af50-c2b78a23e028 · outbound

This paper cites This completes the induction that for all k ≤ min{Tµ, Tξ}, we have ∥wk r,t∥2 = Θ( σ2 0d), ⟨wk r,t, w0 r,t⟩ = Θ(σ2 0d), |⟨wk r,t, µj⟩| = eO(σ0∥µ∥) and |⟨wk r,t, ξi⟩| = eO(σ0σξ √ d).

On the Feature Learning in Diffusion Models This completes the induction that for all k ≤ min{Tµ, Tξ}, we have ∥wk r,t∥2 = Θ( σ2 0d), ⟨wk r,t, w0 r,t⟩ = Θ(σ2 0d), |⟨wk r,t, µj⟩| = eO(σ0∥µ∥) and |⟨wk r,t, ξi⟩| = eO(σ0σξ √ d)

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.143015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.003460Z digest=sha256:9532fe1dfd0d1d5b970a9e771de6308d6130182b700befd5c7d96b73fd928f84

Observation 6e789514-0dfb-46a0-b865-ed8b96f7a7da · outbound

This paper cites This verifies the induction on ∥wk r,t∥2 = Θ(σ2 0d).

On the Feature Learning in Diffusion Models This verifies the induction on ∥wk r,t∥2 = Θ(σ2 0d)

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.128878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.009696Z digest=sha256:72828222ece05acb3e23da5833204228f02c621880eb008678389c10ad8957e6

Observation 5c329a41-658e-4769-9cbb-e6a447a02cf3 · outbound

This paper cites This verifies the induction on ∥wk r,t∥2 = Θ(σ2 0d).

On the Feature Learning in Diffusion Models This verifies the induction on ∥wk r,t∥2 = Θ(σ2 0d)

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:50:59.116391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.014007Z digest=sha256:5d2fc3f4945208574621f33713d54d8204941ea24fbfe9918593bcd7c3370dcd

Observation ff67c990-e495-4b14-a8ec-94ff41a4cb66 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.103615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.018713Z digest=sha256:875b8802e6e2be60c9605ea1e251a4349a6e7a83dafe24cfce400cbc61a3c21b

Observation 4e9f4f04-1c1d-464a-bf8a-33c51a567507 · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.090752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.022903Z digest=sha256:4de3a44b434d7e5ceb679f0208e5ce5fd9ec6c4ce03afc98218cfcb69f1707b8

Observation 272b16a4-a267-46d0-94ce-80d18b47d34d · outbound

This paper cites an unresolved cited work.

On the Feature Learning in Diffusion Models Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:50:59.077603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-12T04:50:59.026954Z digest=sha256:cded866921c6a82af2617d92454ba44df3e19b2daecb8bf48dd28ec06179e40c

Observation 3393d3fb-35a7-47ee-893a-bbad440257bf · outbound

This paper cites Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models.

On the Feature Learning in Diffusion Models Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models

Reference 2021

Resolution
unresolved
no resolver link, observed 2026-08-12T04:50:58.952344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T04:50:58.952344Z digest=sha256:f2d3a00d74a79512d3a06bac0c29b2365652e2088eab694660d875e181fc1af7

Pith citing papers

Observation 83bea2e2-2ca9-4d10-93c4-e53e5db15b70 · inbound

Can Diffusion Models Learn Hidden Inter-Feature Rules Behind Images? cites this paper.

Can Diffusion Models Learn Hidden Inter-Feature Rules Behind Images? On the Feature Learning in Diffusion Models

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-08T21:50:24.513379Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-08T21:50:24.513379Z digest=sha256:68729bf9e51675cc266b9af2123ac215f78730c8bbf4a7689adc9bde38ca0f0b

Observation 8a733580-33fd-48ae-aefb-8fa9b015bcae · inbound

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation cites this paper.

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation On the Feature Learning in Diffusion Models

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-07T13:12:36.894577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T13:12:36.894577Z digest=sha256:52a7bce4988cffdc346228c1ac18905e2c34ff4632f83b3cbb3052d152f701fd

Observation 9471355f-d0fc-4dc3-a845-876620aaefa4 · inbound

Benign Overfitting in Adversarial Training for Vision Transformers cites this paper.

Benign Overfitting in Adversarial Training for Vision Transformers On the Feature Learning in Diffusion Models

Reference 46

Resolution
metadata mismatch
arxiv_id, observed 2026-05-11T12:46:20.621346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-05-10T02:58:29.672338Z digest=sha256:b5ed6b65f3d6b059050048440e49f30b92bc76c038cabfc4c6c17cfdbc90987b

Observation 84a2d645-a780-4633-987a-8688db40f861 · inbound

Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine cites this paper.

Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine On the Feature Learning in Diffusion Models

Reference 23

Resolution
verified exact
arxiv_id, observed 2026-05-21T07:39:49.428181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-05-21T07:36:09.475575Z digest=sha256:0c17d12098d218dd6e1f01cc7e8cab211c3a989cf41ac7a394a95c60c5b8c9a8