Enhancing Diffusion Model Stability for Image Restoration via Gradient Management | Paper Citation Record

Observation 4f626d2f-77d6-4cb8-a8cd-037b76775079 · outbound

This paper cites SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems

Reference 1

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This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:48.697512Z

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 3

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 4

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 5

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.309606Z

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Observation af46af81-d8bb-4c66-a2b1-de19090a1f60 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.280470Z

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Observation 56f81d24-ae6e-40b7-a71f-c8fda1324c3f · outbound

This paper cites Advances in neural information processing systems 36 (2024).

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Advances in neural information processing systems 36 (2024)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:05:01.294594Z

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Observation f8aafcc8-6c9a-4ab0-8f19-a80e8d1c3d9e · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.247331Z

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Observation 6197d4f0-2fee-4480-91fe-34439efad0fb · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.263029Z

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Observation 94bfbb20-3495-4094-98e7-af871e2a0e41 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:49.715527Z

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.232300Z

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Observation 80134c01-89cf-4d23-8bfd-0875b2b2a76c · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.192365Z

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Observation d8768775-1188-4567-ab51-0c27490cca61 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.207798Z

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Observation c510ff5c-704b-460d-8596-4adb0df67cff · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.162072Z

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Observation b461692b-9a9d-4d60-9fc1-0c3fd534a3c7 · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.176547Z

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Observation 17855134-7d94-45e6-8a61-57568ab1599c · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.115889Z

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Observation e1afae78-bff3-42bf-8f56-c54d06f1fc9f · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 18

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.131834Z

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Observation 5851ff60-c5e5-4d44-88d8-2476cc7b020f · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.075065Z

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Observation 2160e924-8536-4af7-9369-b06051b6292e · outbound

This paper cites Fast and Stable Diffusion Inverse Solver with History Gradient Update.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Fast and Stable Diffusion Inverse Solver with History Gradient Update

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:50.551274Z

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Observation d831c078-a058-4143-b868-1b6a3bba71fa · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:50.984409Z

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.089886Z

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Observation 29ce5a38-1992-4fbb-88e1-5af4e8e9a613 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.026453Z

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Observation 280e2050-b965-482d-88b7-1b50399732f0 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:50.904695Z

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Observation 32d72b04-378d-40f7-bfcf-c89ea52509d5 · outbound

This paper cites Decoupled Data Consistency with Diffusion Purification for Image Restoration.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Decoupled Data Consistency with Diffusion Purification for Image Restoration

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:51.400404Z

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Observation e7c5c803-8935-4f7c-bcad-dcab7b236ac5 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.040771Z

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Observation 9603d3d5-6cf1-4860-bb46-5642208c7d9a · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:51.546627Z

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Observation fdb1439d-f65a-4adb-9cd6-7c2db57b5aa4 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:01.011766Z

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Observation 50da6539-a78f-4b4d-badf-269b62f4708a · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.955999Z

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Observation d81e2852-14b3-4e83-ba82-64703ba3b0a4 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.997085Z

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Observation 96dcf450-e9cd-4ca6-b46a-0c90dc529597 · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.926929Z

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Observation b980d0bd-1354-476d-81c4-1d63e250ad49 · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.971923Z

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Observation cbb74338-4846-498d-a60f-57585e01c1f7 · outbound

This paper cites Barron, and Ben Mildenhall.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Barron, and Ben Mildenhall

Reference 34

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.941961Z

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Observation 2db6b266-b473-42ff-b1c8-0df647f4ca1c · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.877082Z

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Observation 1e203e72-511b-4d49-9d6e-3c7ced530253 · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.911858Z

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Observation 1fe7b221-0e94-46f9-a688-d58aaf63e22a · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:52.219433Z

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Observation 2f0bd58d-6cf1-4880-a5f5-da645e1cf5ca · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 39

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Observation fdb6287c-0b11-409a-af8b-8bd2defcd58e · outbound

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Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.808362Z

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Observation accc5838-7a9b-4d61-b30b-88a8757d7960 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.861683Z

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Observation 2eed5f5b-37e1-448b-9a45-13c06802add2 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:52.553170Z

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Observation 1bb67064-3c7c-4ba9-81cd-422c533b6406 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.767540Z

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Observation 58716ca6-4c26-445b-867a-3c17c83246d6 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.823504Z

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Observation c3f55e8a-d3e9-4fb1-8663-a6fa3d9a16b4 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.733970Z

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Observation 0dea7a74-c9ab-4e46-a691-feb2cb5e867a · outbound

This paper cites On Conditioning the Input Noise for Controlled Image Generation with Diffusion Models.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management On Conditioning the Input Noise for Controlled Image Generation with Diffusion Models

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:52.476965Z

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Observation 38061c3a-e85f-4a47-be18-1c8bf1069f9c · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.701622Z

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Observation 5420ae42-e715-4015-95c8-2f063fff9d5c · outbound

This paper cites In MM ’25, October 27–31, 2025, Dublin, Ireland Hongjie Wu et al.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management In MM ’25, October 27–31, 2025, Dublin, Ireland Hongjie Wu et al

Reference 48

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Observation cded9a44-655e-412c-8de3-587bc77c90b8 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.666158Z

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Observation 3ce605df-6c7a-4564-93b9-540dcaaf1981 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.751303Z

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Observation 8c015933-717d-4cb3-9344-f65d7136e753 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.631824Z

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Observation f446be0e-a261-4686-970a-e1c1827570b4 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.717051Z

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Observation dd75c34a-f93d-4b84-8a44-49f8d864cf78 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.597218Z

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Observation c97984f0-8c1a-4721-856c-dc785b98bded · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.683036Z

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Observation edb47e8d-e981-46d8-8e18-515ec4568170 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.563334Z

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Observation e2fb0e4f-1c46-4f4c-9020-a315c81e7c57 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.648303Z

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Observation 91a272d8-724d-4966-be0a-fb76920e728a · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.526318Z

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Observation 5cfe103b-b034-473d-9a33-e603bd5aa722 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.613152Z

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Observation b3a3baa7-118d-4868-80a5-ba75b45018c3 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.048253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d5f9a9d7-b505-4eac-acbc-0a2d5b4b8db1 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.581349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c72035d0-de0e-4858-bedb-1884435fca67 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:54.512253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 572b3859-e5ca-4632-9a01-269daef57a28 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.543998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d5665eca-61eb-4e75-9d3d-545d3c810363 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 63

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:59.206841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b4c2bdcc-6194-4251-ab85-2f07455e7d47 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 64

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:05:00.386640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8a2f5e76-a35f-4852-8ead-fba689e2f2f5 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:55.070179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9ed15f6-7cc1-4751-b1ad-e848ab4d9df4 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 66

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:59.718302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation aef9a00f-e8dd-41b5-a771-e040396b1f04 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:57.662839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a5357c58-6068-4d6d-be1a-994548f6e000 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:59.389612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c387a543-c79f-4a9b-bc1d-719578d89b20 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 69

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:57.098482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5780ede4-04a1-43e1-aab7-181c30faea85 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 70

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:58.924323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f29114b9-e2f0-46b4-a5d7-3d2aea6c845e · outbound

This paper cites In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:58.604904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4652ec34-3cc5-4001-8813-3910de654880 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 74

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:57.993682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation daaa938c-3eef-42b1-8462-520eb92fe1ed · outbound

This paper cites Efros, Eli Shechtman, and Oliver Wang.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Efros, Eli Shechtman, and Oliver Wang

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:55.412612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6559bca7-7774-4516-bf96-427d7399c699 · outbound

This paper cites 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (2018), 586–595.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (2018), 586–595

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:57.477959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0654ba96-1755-4eaa-b7a2-54faa824c851 · outbound

This paper cites an unresolved cited work.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Unresolved cited work

Reference 79

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:04:56.761226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0425cbb1-545a-46db-b883-e9cb110ea163 · outbound

This paper cites B Proofs B.1 Descent Lemma for L-Smooth Functions To support the proof of Proposition 4.1, we first state and prove the following lemma concerning functions with 𝐿-smooth gradients.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management B Proofs B.1 Descent Lemma for L-Smooth Functions To support the proof of Proposition 4.1, we first state and prove the following lemma concerning functions with 𝐿-smooth gradients

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:56.505330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 068153ad-9e35-4e43-a6b0-13abd0e6d5d1 · outbound

This paper cites By the Fundamental Theorem of Calculus for vector functions, we have: 𝑓(w′)− 𝑓(w) = ∫ 1 0 ⟨∇𝑓(w+ 𝑡(w′− w)), w′− w⟩ 𝑑𝑡.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management By the Fundamental Theorem of Calculus for vector functions, we have: 𝑓(w′)− 𝑓(w) = ∫ 1 0 ⟨∇𝑓(w+ 𝑡(w′− w)), w′− w⟩ 𝑑𝑡

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:56.278395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b7ce51e2-bb28-458c-b35d-56ee3ecc4c80 · outbound

This paper cites Thus, each warm-up step guarantees a non-increasing likelihood objective, 𝐿𝑡(x(𝑗+1) 𝑡 )≤ 𝐿𝑡(x(𝑗) 𝑡 ), with strict decrease if g𝑙(x(𝑗) 𝑡 ) ≠ 0.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Thus, each warm-up step guarantees a non-increasing likelihood objective, 𝐿𝑡(x(𝑗+1) 𝑡 )≤ 𝐿𝑡(x(𝑗) 𝑡 ), with strict decrease if g𝑙(x(𝑗) 𝑡 ) ≠ 0

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:56.127158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 38c77a03-a1ce-4124-abfb-df0e00895b5e · outbound

This paper cites International journal of computer vision 115 (2015), 211–252.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management International journal of computer vision 115 (2015), 211–252

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:52.285623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30e6c2f0-2b5c-48b9-86ac-2741a6a31e95 · outbound

This paper cites In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:04:58.262233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bf5c15b0-ba5d-4ef9-9483-c591c754558f · outbound

This paper cites Neural Processing Letters 51 (2020), 2007–2028.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management Neural Processing Letters 51 (2020), 2007–2028

Reference 2020

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:05:01.146634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ac49e202-e7e8-4126-99a5-c776dbae2b61 · outbound

This paper cites In Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition.

Enhancing Diffusion Model Stability for Image Restoration via Gradient Management In Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:48.816266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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