Paper Citation Record · LEDGER

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations

As of 9 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2512.14980.

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

pith.paper-citation-record.v1
2512.14980 v4

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T15:59:13.843182Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

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unresolved18
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External citation measurements

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Outbound references

Observation 9a9d8c68-8369-4105-85c6-0ce4e464087a · outbound

This paper cites Karnakov, P., Litvinov, S., and Koumoutsakos, P.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Karnakov, P., Litvinov, S., and Koumoutsakos, P

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.057925Z

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Unavailable: canonical work link unavailable.

Observation 87ff3e33-cb02-4259-b05b-fa53f1c26575 · outbound

This paper cites Following these results, we use the truncated log-normal distribution for all our experiments.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Following these results, we use the truncated log-normal distribution for all our experiments

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.513113Z

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Observation ad3c67ae-f912-4667-884b-dbc4efbf7c8b · outbound

This paper cites Helmholtz Equation For the Helmholtz Equation we used the UNet implementation by Karras et al.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Helmholtz Equation For the Helmholtz Equation we used the UNet implementation by Karras et al

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.728280Z

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Observation 1a4e9c98-2615-478e-8d9a-70dd3906fa3d · outbound

This paper cites Table 7.Runtimes of vanilla and our method on training and sampling on an NVIDIA H200 GPU.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Table 7.Runtimes of vanilla and our method on training and sampling on an NVIDIA H200 GPU

Reference 7

Resolution: malformed identifier; no resolver link, observed 2026-08-03T15:59:13.843182Z

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Observation 37cba9ad-8990-4a1d-8526-f7b56ee6ae69 · outbound

This paper cites Bastek et al.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Bastek et al

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.714199Z

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Observation dfcba813-b539-467e-8258-189f11359fd3 · outbound

This paper cites Injecting Measurement Structure for Training Inverse Problem SolversMathematically, the closest work is the likelihood-informed Doob’s h-transform by Denker et al.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Injecting Measurement Structure for Training Inverse Problem SolversMathematically, the closest work is the likelihood-informed Doob’s h-transform by Denker et al

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.806395Z

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Observation 7e6fca85-5f2a-4208-8495-420852884fe3 · outbound

This paper cites dual path.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations dual path

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.920200Z

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Observation ec69d0f1-194d-477b-b4b6-2b6240aa6b41 · outbound

This paper cites We take p(xT ) to be approximately N(0, σ2 maxI), i.e.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations We take p(xT ) to be approximately N(0, σ2 maxI), i.e

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.002734Z

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Observation feff8a53-a897-4073-8b29-0e725fd228d7 · outbound

This paper cites fine-grained.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations fine-grained

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.096284Z

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Observation 348f6dab-3811-488c-81b9-748d8cb093e4 · outbound

This paper cites an unresolved cited work.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.189562Z

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Observation 0dd5cf48-96f1-4a25-ae4d-87d0b411b06c · outbound

This paper cites intermediate.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations intermediate

Reference 100

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.379943Z

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Observation 76aa541e-e3d1-4d7d-961f-7425a30e3d52 · outbound

This paper cites an unresolved cited work.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Unresolved cited work

Reference 128

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:13.611346Z

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Observation 459207ba-6f1c-4e69-95a5-5a67d5404bd2 · outbound

This paper cites Song, J., Vahdat, A., Mardani, M., and Kautz, J.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Song, J., Vahdat, A., Mardani, M., and Kautz, J

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.449667Z

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Observation 7ef05652-1d33-4046-8129-45a4b3c6eb5b · outbound

This paper cites C., Azizzadenesheli, K., and Anandkumar, A.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations C., Azizzadenesheli, K., and Anandkumar, A

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.548403Z

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Observation d66fe5b1-b178-428e-be74-d47915b5d802 · outbound

This paper cites an unresolved cited work.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Unresolved cited work

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.251137Z

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Observation 55f3dece-150f-435d-8542-0f188853c133 · outbound

This paper cites Analyzing and Improving the Training Dy- namics of Diffusion Models.2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Analyzing and Improving the Training Dy- namics of Diffusion Models.2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.163407Z

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Observation fe636cc9-cce7-49d5-aa5b-fb1b87c08574 · outbound

This paper cites Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.336001Z

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Observation d367822e-017e-4daa-99a9-b77a0eb94ab9 · outbound

This paper cites Proofs Proposition 3.1.Let D∗ reg(xt, t)be the denoiser that minimizes the regularized objective Lreg.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Proofs Proposition 3.1.Let D∗ reg(xt, t)be the denoiser that minimizes the regularized objective Lreg

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:12.635696Z

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Unavailable: canonical work link unavailable.

Observation 14e91450-802b-4a7e-879d-a6306a35cb3d · outbound

This paper cites Bastek, J.-H., Sun, W., and Kochmann, D.

Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations Bastek, J.-H., Sun, W., and Kochmann, D

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-03T15:59:11.989619Z

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Pith citing papers

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