Paper Citation Record · LEDGER

Generalization bounds for score-based generative models: a synthetic proof

As of 10 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 7 inbound Pith citation observations for arXiv:2507.04794.

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

pith.paper-citation-record.v1
2507.04794 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:54:30.346841Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T21:43:02.233153Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T21:45:05.649781Z

Reference resolution

25 of 25 outbound references displayed

verified exact2
verified fuzzy4
unresolved18
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a6e1d427-a58e-4858-95cd-29806c8255d0 · outbound

This paper cites From the mean value theorem, we have ∥s⋆(t, x)∥ ≤ ∥∇s⋆(t, ·)∥∞∥x − x⋆∥ + ∥s⋆(t, x⋆)∥.

Generalization bounds for score-based generative models: a synthetic proof From the mean value theorem, we have ∥s⋆(t, x)∥ ≤ ∥∇s⋆(t, ·)∥∞∥x − x⋆∥ + ∥s⋆(t, x⋆)∥

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:54:32.782853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 382ac3a5-53c8-47c4-bbae-75bfaa5f2daf · outbound

This paper cites an unresolved cited work.

Generalization bounds for score-based generative models: a synthetic proof Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:54:32.620896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3cc67535-d57f-4298-95a8-b307bd806540 · outbound

This paper cites doi: 10.1093/acprof:oso/9780199535255.001.0001.

Generalization bounds for score-based generative models: a synthetic proof doi: 10.1093/acprof:oso/9780199535255.001.0001

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.362821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9eaf397c-de94-40ba-87f0-76fefa980ecb · outbound

This paper cites Beyond log-concavity and score regularity: Improved convergence bounds for score-based generative models in w2-distance.arXiv preprint arXiv:2501.02298,.

Generalization bounds for score-based generative models: a synthetic proof Beyond log-concavity and score regularity: Improved convergence bounds for score-based generative models in w2-distance.arXiv preprint arXiv:2501.02298,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.682049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5bc0fc78-99ed-4052-8048-857b9867dc00 · outbound

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

Generalization bounds for score-based generative models: a synthetic proof DiffWave: A Versatile Diffusion Model for Audio Synthesis

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.819255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a471c99c-1c7e-454c-beb9-3b33601a312a · outbound

This paper cites Nonparametric estimation of a factorizable density using diffusion models.arXiv preprint arXiv:2501.01783,.

Generalization bounds for score-based generative models: a synthetic proof Nonparametric estimation of a factorizable density using diffusion models.arXiv preprint arXiv:2501.01783,

Reference 12

Resolution: verified exact; raw_fallback, observed 2026-08-06T19:54:30.807887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation daea18f6-55fb-41a7-b24f-db1488bf6343 · outbound

This paper cites Score-Based Generative Modeling through Stochastic Differential Equations.

Generalization bounds for score-based generative models: a synthetic proof Score-Based Generative Modeling through Stochastic Differential Equations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:29.215888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c4d69c0-aaa7-47d1-9768-027b13bc3dec · outbound

This paper cites Smooth transport map via diffusion process.

Generalization bounds for score-based generative models: a synthetic proof Smooth transport map via diffusion process

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:29.297105Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1119d330-272e-46a3-9f7d-2419465325fc · outbound

This paper cites Regularity of the score function in generative models.

Generalization bounds for score-based generative models: a synthetic proof Regularity of the score function in generative models

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:29.354919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69fa950a-2e23-4c6d-8b2d-b0348b40bce2 · outbound

This paper cites Generalization error bound for denoising score matching under relaxed manifold assumption.

Generalization bounds for score-based generative models: a synthetic proof Generalization error bound for denoising score matching under relaxed manifold assumption

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:29.510458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b39bfc82-5c8e-4d48-8bc2-4c3930147147 · outbound

This paper cites Then it holds EX∼p⋆ bf (X) = (EX∼p⋆ − En) bf (X) + En bf (X) ≤ (EX∼p⋆ − En) bf (X) + En ¯f (X) = EX∼p⋆ ¯f (X) + (EX∼p⋆ − En) bf (X) + (En − EX∼p⋆) ¯f (X).

Generalization bounds for score-based generative models: a synthetic proof Then it holds EX∼p⋆ bf (X) = (EX∼p⋆ − En) bf (X) + En bf (X) ≤ (EX∼p⋆ − En) bf (X) + En ¯f (X) = EX∼p⋆ ¯f (X) + (EX∼p⋆ − En) bf (X) + (En − EX∼p⋆) ¯f (X)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:54:32.246053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 303a02ec-d7b2-4413-8a6b-809dfe9047e8 · outbound

This paper cites an unresolved cited work.

Generalization bounds for score-based generative models: a synthetic proof Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:54:32.084838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 02f6f2dc-63a1-4a00-905b-a2d653996a7f · outbound

This paper cites First of all, the caset > C−1 ⋆ log(ε−1)−C⋆ is immediate.

Generalization bounds for score-based generative models: a synthetic proof First of all, the caset > C−1 ⋆ log(ε−1)−C⋆ is immediate

Reference 20

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T19:54:32.443511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 53a56a4b-3fce-4916-b763-4f33de89c5d4 · outbound

This paper cites Proof of Theorem II.As a base density, let us choose the standard gaussian g0(x) := (2π)−d/2 exp(−∥x∥2/2).

Generalization bounds for score-based generative models: a synthetic proof Proof of Theorem II.As a base density, let us choose the standard gaussian g0(x) := (2π)−d/2 exp(−∥x∥2/2)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:54:31.895178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3c5c4129-7058-4cfa-bd43-7418d0f7bc13 · outbound

This paper cites Its integral is trivially equal to one.

Generalization bounds for score-based generative models: a synthetic proof Its integral is trivially equal to one

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:54:31.712556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 84545a22-1346-4d15-a19d-b4a544ad0f8c · outbound

This paper cites an unresolved cited work.

Generalization bounds for score-based generative models: a synthetic proof Unresolved cited work

Reference 104

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:54:31.582693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e9c142e2-377a-462e-a619-ad3e9ec5a6eb · outbound

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

Generalization bounds for score-based generative models: a synthetic proof Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions

Reference 1982

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.161064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e70c02d5-3a18-4409-aef9-370aaf24ae5b · outbound

This paper cites doi: 10.1214/aos/1032894451.

Generalization bounds for score-based generative models: a synthetic proof doi: 10.1214/aos/1032894451

Reference 1996

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.510488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8f70cbb-5d5a-4121-9e8e-64047408f109 · outbound

This paper cites Error Bounds for Flow Matching Methods.

Generalization bounds for score-based generative models: a synthetic proof Error Bounds for Flow Matching Methods

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.295830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24c70396-8689-48e7-86bf-fcc3eae8737d · outbound

This paper cites Flow matching achieves almost minimax optimal convergence.

Generalization bounds for score-based generative models: a synthetic proof Flow matching achieves almost minimax optimal convergence

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.606444Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ada3be6e-ad31-48a7-8357-ad05cd526d78 · outbound

This paper cites On the minimax optimality of flow matching through the connection to kernel density estimation.

Generalization bounds for score-based generative models: a synthetic proof On the minimax optimality of flow matching through the connection to kernel density estimation

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.896720Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29147224-0917-476e-a352-e846bf5b954d · outbound

This paper cites Convergence Analysis of Probability Flow ODE for Score-based Generative Models.

Generalization bounds for score-based generative models: a synthetic proof Convergence Analysis of Probability Flow ODE for Score-based Generative Models

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.749964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2cc64cfc-6ecb-4641-b265-3497e513bea1 · outbound

This paper cites A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models.

Generalization bounds for score-based generative models: a synthetic proof A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:29.088405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5df27305-dc7b-4256-990c-48c9f1f5732a · outbound

This paper cites Adapted wasserstein distance between the laws of sdes.arXiv preprint arXiv:2209.03243,.

Generalization bounds for score-based generative models: a synthetic proof Adapted wasserstein distance between the laws of sdes.arXiv preprint arXiv:2209.03243,

Reference 2024

Resolution: verified exact; raw_fallback, observed 2026-08-06T19:54:31.373656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 34fb8965-2aa1-4790-b89f-42495f310844 · outbound

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

Generalization bounds for score-based generative models: a synthetic proof Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-06T19:54:28.431554Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation f746632c-b078-497a-a3a9-28f14281eb42 · inbound

Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities cites this paper.

Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities Generalization bounds for score-based generative models: a synthetic proof

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:10:55.359443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b201491-db1d-4d61-8889-97bddf9ae90e · inbound

Statistical Analysis of Markovian Generative Modeling cites this paper.

Statistical Analysis of Markovian Generative Modeling Generalization bounds for score-based generative models: a synthetic proof

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-11T20:26:10.019831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7d3997ca-e4c9-47f9-a9f7-8382dd929315 · inbound

Understanding diffusion models requires rethinking (again) generalization cites this paper.

Understanding diffusion models requires rethinking (again) generalization Generalization bounds for score-based generative models: a synthetic proof

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-05-11T18:46:10.665812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d0d09cf8-ea11-4fba-a951-6ab57d3c1ddc · inbound

Statistical Convergence of Spherical First Hitting Diffusion Models cites this paper.

Statistical Convergence of Spherical First Hitting Diffusion Models Generalization bounds for score-based generative models: a synthetic proof

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:15:58.197615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 908cf375-dd88-42e8-9076-f30464c3a009 · inbound

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training cites this paper.

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training Generalization bounds for score-based generative models: a synthetic proof

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:12:51.183017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e1f57146-7548-48c8-9f67-94382f8acc4b · inbound

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training cites this paper.

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training Generalization bounds for score-based generative models: a synthetic proof

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-06-30T21:45:05.651381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aaf789ec-fe34-44a5-9836-38c74865f962 · 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 Generalization bounds for score-based generative models: a synthetic proof

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-20T20:53:43.747417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.