Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-26T00:21:04.782902Z
Paper Citation Record · LEDGER
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space
As of 23 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2606.24157.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
49 of 49 outbound references displayed
- verified exact4
- verified fuzzy0
- unresolved45
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5bfb8a54-121b-4d7b-bade-72d32df90e69 · outbound
This paper cites It is the equation of motion in Wasserstein space.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space It is the equation of motion in Wasserstein space
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3fe42c96-65a8-416f-9f43-00c40b660765 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4b45f04f-0a6a-492f-a1f5-5155719ee565 · outbound
This paper cites ˙ρ=−gradW F(ρ).
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space ˙ρ=−gradW F(ρ)
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cec16f89-3513-45d6-9ac7-13c2105deb00 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c719863f-7fc3-4ed9-bc1b-45627befd7ec · outbound
This paper cites (1781).M´ emoire sur la th´ eorie des d´ eblais et des remblais.Histoire de l’Acad´ emie Royale des Sciences de Paris, 666–704.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (1781).M´ emoire sur la th´ eorie des d´ eblais et des remblais.Histoire de l’Acad´ emie Royale des Sciences de Paris, 666–704
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 21b7a54a-e917-45bb-a871-1bd47e1a271d · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 22f7d7d2-3044-4df2-b3b7-cf1a592f3915 · outbound
This paper cites (1991).Polar factorization and monotone rearrangement of vector-valued functions.Comm.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (1991).Polar factorization and monotone rearrangement of vector-valued functions.Comm
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d91cf69c-2eec-4813-bfed-3488ae81d0b2 · outbound
This paper cites Wasserstein distance.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Wasserstein distance
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e66f5472-c4b9-48f7-8bea-858c3554e734 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3781693a-8fe6-429f-8fb1-157422ea4d08 · outbound
This paper cites & Brenier, Y.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Brenier, Y
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8716893b-bef9-4ddb-9af7-fde58ce6240d · outbound
This paper cites (1998).The variational formulation of the Fokker–Planck equation.SIAM J.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (1998).The variational formulation of the Fokker–Planck equation.SIAM J
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e7d28870-efa5-4707-be4a-2fd6f628173a · outbound
This paper cites (2001).The geometry of dissipative evolution equations: the porous medium equation.Comm.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2001).The geometry of dissipative evolution equations: the porous medium equation.Comm
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 95458fa3-067c-4c72-b121-2f6b139e92bf · outbound
This paper cites (2008).Gradient Flows in Metric Spaces and in the Space of Probability Measures.Birkh¨ auser.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2008).Gradient Flows in Metric Spaces and in the Space of Probability Measures.Birkh¨ auser
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation adb4fdce-04c6-452a-b941-093a4f1b01a5 · outbound
This paper cites (2003).Topics in Optimal Transportation.AMS.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2003).Topics in Optimal Transportation.AMS
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 17cfef75-5d73-4839-a84e-a19e52d0e5d9 · outbound
This paper cites (2015).Optimal Transport for Applied Mathematicians.Birkh¨ auser.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2015).Optimal Transport for Applied Mathematicians.Birkh¨ auser
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8760b78f-77e0-4a83-bac8-577d8f1f4f8b · outbound
This paper cites & Cuturi, M.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Cuturi, M
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d4ba500a-a941-4984-8e60-e3fb6935a1d1 · outbound
This paper cites & Santambrogio, F.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Santambrogio, F
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 336ed51e-ddbc-41de-acb8-dd59c25349e2 · outbound
This paper cites (2021).Large- scale Wasserstein gradient flows.NeurIPS.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2021).Large- scale Wasserstein gradient flows.NeurIPS
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f31a5feb-64db-4553-81ef-effa20c21c80 · outbound
This paper cites (2023).Normalizing flow neural networks by JKO scheme.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2023).Normalizing flow neural networks by JKO scheme
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f8ef443-971a-4110-be3d-c0a2da6ddf7f · outbound
This paper cites (2005).Estimation of non-normalized statistical models by score matching.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2005).Estimation of non-normalized statistical models by score matching
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6feb65ff-c71c-4018-adf5-cb374b4a55ca · outbound
This paper cites (2011).A connection between score matching and denoising autoencoders.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2011).A connection between score matching and denoising autoencoders
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5a95df5f-7637-4d4f-b132-a7a3ada9d625 · outbound
This paper cites & Teh, Y.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Teh, Y
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d0bbc3a6-4090-42cc-8e95-9f015e2af6ed · outbound
This paper cites & Ermon, S.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Ermon, S
Reference 23
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2f1571b7-7ae3-4f28-bb48-2a1447e96b5b · outbound
This paper cites (2020).Denoising diffusion probabilistic models.NeurIPS.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2020).Denoising diffusion probabilistic models.NeurIPS
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 69a24b81-94d0-4951-b803-dfdbb7795db6 · outbound
This paper cites (2021).Denoising diffusion implicit models.ICLR.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2021).Denoising diffusion implicit models.ICLR
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation eddcdc17-8242-4c3c-9644-85429a508bfc · outbound
This paper cites P., Kumar, A., Ermon, S., & Poole, B.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space P., Kumar, A., Ermon, S., & Poole, B
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f38ff38e-d740-4362-ba23-63559e9ab7f1 · outbound
This paper cites (2022).Elucidating the design space of diffusion-based generative models.NeurIPS.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (2022).Elucidating the design space of diffusion-based generative models.NeurIPS
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a085a474-d254-479e-8d62-aa6bd2bd1f47 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d8394fb2-577f-497c-9682-3f3ca889a93d · outbound
This paper cites Energy matching: Unifying flow matching and energy-based models for generative modeling.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Energy matching: Unifying flow matching and energy-based models for generative modeling
Reference 29
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T16:39:57.924494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2a5b6730-0fea-406b-b091-ade1c02a4746 · outbound
This paper cites Equilibrium matching: Generative modeling with implicit energy-based models.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Equilibrium matching: Generative modeling with implicit energy-based models
Reference 30
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T16:39:57.927468Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e5b4d206-ff20-4cd1-8abb-24270fb3ae9e · outbound
This paper cites S., Boffi, N.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space S., Boffi, N
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d59fe256-3e00-4d87-8473-73bc9673410e · outbound
This paper cites Flow Matching Guide and Code.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Flow Matching Guide and Code
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-07-04T16:39:57.915199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9d5c1e78-779a-438f-8e20-ee874f7c06bf · outbound
This paper cites Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching
Reference 33
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T16:39:57.925571Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ad62e94e-0ccb-4b84-82dd-c4368d30ccb3 · outbound
This paper cites & Erives, E.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Erives, E
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9f1c3ad4-e07c-43e2-96fb-4537ed5a3e6e · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9ef570c3-0660-444a-adcf-691d95974f74 · outbound
This paper cites (1908).Sur la th´ eorie du mouvement brownien.C.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (1908).Sur la th´ eorie du mouvement brownien.C
Reference 36
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a758e43b-7f40-43af-842d-187459056519 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 37
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- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 02962943-6835-4eff-a764-99685f372087 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7f92b414-5f90-4030-a769-7e587a86fcb7 · outbound
This paper cites (1951).On stochastic differential equations.Mem.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space (1951).On stochastic differential equations.Mem
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f18b731-7c8f-4082-956c-d7d2327d97af · outbound
This paper cites & Leibler, R.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space & Leibler, R
Reference 40
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e8ec43d-1a41-40d8-8547-2335beec747e · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 41
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- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 018638cf-1277-4997-9d1f-b83474fa89c0 · outbound
This paper cites assigning size to sets.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space assigning size to sets
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a0ecb12-519e-40ed-9ee7-b7f16ead8b06 · outbound
This paper cites the densityρ(x) being large at some point.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space the densityρ(x) being large at some point
Reference 43
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 467de97d-0110-4622-a906-4f283f74c08e · outbound
This paper cites transposing.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space transposing
Reference 44
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 04b38457-9bac-4de1-84aa-b8e87d2e5396 · outbound
This paper cites an unresolved cited work.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space Unresolved cited work
Reference 45
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 79c7da21-d531-4804-99c6-a247821eb9d2 · outbound
This paper cites rolling downhill.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space rolling downhill
Reference 46
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 68232b33-b1ee-4429-8d8e-ef46359ff57d · outbound
This paper cites gradient direction.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space gradient direction
Reference 47
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e2e6594-a455-4301-aac3-14acdea48e37 · outbound
This paper cites It is the standard tool for proving stability.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space It is the standard tool for proving stability
Reference 48
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fd8c9f89-cb4c-46e0-8b6b-446d7488a05a · outbound
This paper cites gradient equals zero.
The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space gradient equals zero
Reference 49
- Resolution
- unresolved
- no resolver link, observed 2026-06-26T00:21:04.782902Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.