Papers › Generative Modeling by Estimating Gradients of the Data Distribution
Generative Modeling by Estimating Gradients of the Data Distribution
Yang Song, Stefano Ermon
We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="1907.05600")
Code
Syntology Ran 14 of 22 code samples harvested from 8 repositories linked to this paper; 8 have no recorded run. Of those that ran: 1 ran · honoured contract; 1 ran · our draft was wrong; 2 ran · fixture could not drive it; 10 ran with no contract checked.
By repository: community (archive-listed): 22 samples from 8 repositories, 14 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
13 repositories listed; official and paper-mentioned ones first.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
22 samples harvested; 14 ran; 1 honoured the contract we drafted; 8 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 9 of the 22 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from 8 repositories linked to this paper, official or community; each sample names its own and says which. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
a36c0d3f631164cf · report
b67d9759d330f8e9 · report
543e9573790e3f36 · report
28b6b8fdea88c99d · report
d217a4b1f1925355 · report
f02dfb63731445ee · report
55fdb754c0cda85c · report
495f6791fda7d15e · report
04ab830c8352fa59 · report
2ceaba81d90f5640 · report
cff1bdc3f34eb185 · report
7c385bfdbcac9ebc · report
05f3653dd76468d9 · report
308c9ffe9425921a · report
2985c25add4b01dc · report
9979dc271f83e97a · report
2149b8836f88ca16 · report
45b72aead272b1d0 · report
4208709a6798c6ab · report
c0db9b95b0194d7a · report
1a2134b893169239 · report
9a46fa84765de343 · report
Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Generation | CIFAR-10 | NCSN | FID | 25.32 | #63 of 78 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
Introduced by this paper: Denoising Score Matching
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections