--- title: AI Paper Review: Generative Modeling by Estimating... description: A deep-dive review of the 2019 paper 'Generative Modeling by Estimating Gradients of the Data Distribution' by Yang Song and Stefano Ermon, which introduced... canonical: https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution | daily.dev og:description: A deep-dive review of the 2019 paper 'Generative Modeling by Estimating Gradients of the Data Distribution' by Yang Song and Stefano Ermon, which introduced... og:url: https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey og:image: https://api.daily.dev/og/posts/AOAzfpQEy.png og:image:alt: AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution **[freeCodeCamp](https://daily.dev/sources/freecodecamp)** · 34 min read · 1 upvotes · 0 comments ## Summary A deep-dive review of the 2019 paper 'Generative Modeling by Estimating Gradients of the Data Distribution' by Yang Song and Stefano Ermon, which introduced score-based generative modeling. The review walks through the paper's core ideas: learning the score (gradient of log-density) instead of the data distribution directly, the challenges posed by the manifold hypothesis and low-density regions, and the proposed solutions—Noise Conditional Score Networks (NCSNs) and annealed Langevin dynamics. It covers denoising and sliced score matching, experimental results on MNIST, CelebA, and CIFAR-10 (including a state-of-the-art Inception Score of 8.87 on CIFAR-10), image inpainting applications, and the paper's lasting legacy in shaping modern diffusion models like DDPM, Score-SDE, Imagen, and Stable Diffusion. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### What is score-based generative modeling and how does it differ from GANs or likelihood-based models? Score-based generative modeling learns the score, the gradient of the log data density, instead of modeling the data distribution or its likelihood directly. New samples are generated by starting from random noise and following the learned score via Langevin dynamics. This avoids adversarial training (unlike GANs) and restrictive architectures (unlike likelihood-based models), while providing a tractable training objective. _Explore more breakdowns of foundational generative modeling papers like this on daily.dev._ ### Why does naive score matching fail on real image data like CIFAR-10? Naive score matching fails because real images lie on low-dimensional manifolds embedded in high-dimensional space, making the score undefined outside the manifold where density is zero. Training a sliced score matching model directly on CIFAR-10 causes the loss to fluctuate and fail to converge; adding a small amount of Gaussian noise gives the data full support and restores stable convergence. _daily.dev helps developers dig into the math behind generative model training pitfalls like this._ ### What are Noise Conditional Score Networks (NCSNs) and how do they use annealed Langevin dynamics? Noise Conditional Score Networks are a single neural network conditioned on noise level that learns the score function across a whole spectrum of Gaussian perturbations, from heavily corrupted to nearly clean data. Annealed Langevin dynamics then samples by starting from pure noise and stepping through decreasing noise levels, using each level's score to refine the sample, achieving an Inception Score of 8.87 and FID of 25.32 on CIFAR-10. _daily.dev surfaces deep technical walkthroughs like this for engineers tracking diffusion model internals._ ## Similar posts on daily.dev - [AI Paper Review: Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v) · freeCodeCamp · 0 upvotes · 0 comments --- Tags: [#machine-learning](https://daily.dev/tags/machine-learning), [#genai](https://daily.dev/tags/genai), [#diffusion-models](https://daily.dev/tags/diffusion-models) [View this post on daily.dev](https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution","url":"https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey"},"datePublished":"2026-08-12T22:56:44.391Z","dateModified":"2026-09-14T06:41:34.699Z","description":"A deep-dive review of the 2019 paper 'Generative Modeling by Estimating Gradients of the Data Distribution' by Yang Song and Stefano Ermon, which introduced...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/d061af27329274fe82ce08867e48844a?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/d061af27329274fe82ce08867e48844a?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"freeCodeCamp","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"freeCodeCamp","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1628412854/logos/freecodecamp","url":"https://daily.dev/sources/freecodecamp"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":1},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"machine-learning,genai,diffusion-models","timeRequired":"PT34M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"freeCodeCamp","item":"https://daily.dev/sources/freecodecamp"},{"@type":"ListItem","position":3,"name":"AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey#faq","mainEntity":[{"@type":"Question","name":"What is score-based generative modeling and how does it differ from GANs or likelihood-based models?","acceptedAnswer":{"@type":"Answer","text":"Score-based generative modeling learns the score, the gradient of the log data density, instead of modeling the data distribution or its likelihood directly. 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