--- title: AI Paper Review: Deep Unsupervised Learning using... description: A detailed review of the 2015 paper 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Sohl-Dickstein et al., which introduced diffusion... canonical: https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: AI Paper Review: Deep Unsupervised Learning using Nonequilibrium Thermodynamics | daily.dev og:description: A detailed review of the 2015 paper 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Sohl-Dickstein et al., which introduced diffusion... og:url: https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v og:image: https://api.daily.dev/og/posts/WgHs7AX5v.png og:image:alt: AI Paper Review: Deep Unsupervised Learning using Nonequilibrium Thermodynamics 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: Deep Unsupervised Learning using Nonequilibrium Thermodynamics **[freeCodeCamp](https://daily.dev/sources/freecodecamp)** · 27 min read · 0 upvotes · 0 comments ## Summary A detailed review of the 2015 paper 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Sohl-Dickstein et al., which introduced diffusion probabilistic models (DPMs). The review covers the paper's core motivation — overcoming the tractability-vs-expressiveness trade-off in generative modeling — and walks through the full algorithm: the forward diffusion process that gradually corrupts data into noise, the reverse process that learns to reconstruct data, the training objective (a variational lower bound on log-likelihood), diffusion rate scheduling, and posterior inference via conditional generation. Experiments on Swiss Roll, Binary Heartbeat, MNIST, CIFAR-10, Dead Leaves, and Bark textures are summarized. The review contextualizes the paper as the mathematical foundation for modern diffusion models like Stable Diffusion and DALL·E. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### What is the original paper that introduced diffusion probabilistic models used by Stable Diffusion and DALL-E? The foundational paper is 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Jascha Sohl-Dickstein and collaborators, published in 2015. It introduced the first practical formulation of diffusion probabilistic models by defining a forward process that gradually adds noise to data and a reverse process that learns to remove it, drawing on nonequilibrium statistical physics concepts like Langevin dynamics and the Fokker-Planck equation. _daily.dev surfaces foundational AI research like this for engineers building on diffusion models._ ### How does the training objective for diffusion probabilistic models work mathematically? Training maximizes a tractable lower bound on the log-likelihood derived using Jensen's inequality, similar to the variational objective used in VAEs. This bound is computed through KL divergence and entropy terms, and it becomes progressively tighter as forward and reverse diffusion steps get smaller, eventually matching the true likelihood in the quasi-static limit where each step is infinitesimally small. _daily.dev helps engineers studying generative model training objectives dig into the underlying math._ ### How do diffusion models perform image inpainting and denoising without a separate module? Diffusion models handle inpainting and denoising by multiplying each intermediate reverse-process distribution by a conditioning function representing known pixels or constraints, rather than adding a separate inference step after generation. Known pixels are treated as fixed while unknown regions continue evolving through the reverse diffusion trajectory, letting conditioning integrate directly into each small reverse transition. _daily.dev keeps builders working on conditional image generation close to research explaining the mechanics._ ## Similar posts on daily.dev - [AI Paper Review: Generative Modeling by Estimating Gradients of the Data Distribution](https://daily.dev/posts/ai-paper-review-generative-modeling-by-estimating-gradients-of-the-data-distribution-aoazfpqey) · freeCodeCamp · 1 upvotes · 0 comments - [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://daily.dev/posts/overcoming-dimensional-factorization-limits-in-discrete-diffusion-models-through-quantum-joint-distr-xff3xbyei) · Nature · 0 upvotes · 0 comments - [A Theory of Deep Learning](https://daily.dev/posts/a-theory-of-deep-learning-sag1w2qug) · Hacker News · 2 upvotes · 0 comments --- Tags: [#deep-learning](https://daily.dev/tags/deep-learning), [#genai](https://daily.dev/tags/genai), [#unsupervised-learning](https://daily.dev/tags/unsupervised-learning), [#diffusion-models](https://daily.dev/tags/diffusion-models) [View this post on daily.dev](https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v) ```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: Deep Unsupervised Learning using Nonequilibrium Thermodynamics","url":"https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v"},"datePublished":"2026-07-15T18:41:55.988Z","dateModified":"2026-09-13T19:15:08.261Z","description":"A detailed review of the 2015 paper 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Sohl-Dickstein et al., which introduced diffusion...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/52f530b1c004875811b9cd88bc6e371c?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/52f530b1c004875811b9cd88bc6e371c?_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-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"deep-learning,genai,unsupervised-learning,diffusion-models","timeRequired":"PT27M"} {"@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: Deep Unsupervised Learning using Nonequilibrium Thermodynamics"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/ai-paper-review-deep-unsupervised-learning-using-nonequilibrium-thermodynamics-wghs7ax5v#faq","mainEntity":[{"@type":"Question","name":"What is the original paper that introduced diffusion probabilistic models used by Stable Diffusion and DALL-E?","acceptedAnswer":{"@type":"Answer","text":"The foundational paper is 'Deep Unsupervised Learning using Nonequilibrium Thermodynamics' by Jascha Sohl-Dickstein and collaborators, published in 2015. 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