Diffusion models

Working Definition

A diffusion model is a generative model trained to reverse a gradual data-destruction process: Gaussian noise is added to an image, audio signal, or molecular structure across many small steps until only pure noise remains, and a neural network learns to undo each step. Generation begins by sampling random noise and passing it through the learned sequence of denoising steps toward a sample that resembles the training distribution. Technically, at each noise level the network approximates the gradient of the log probability density of the data (the score function), meaning it never computes the global probability of an image directly, but always knows “which direction” leads toward higher probability. In popular usage, the term has become synonymous with text-to-image generators (Stable Diffusion, Midjourney, DALL·E), obscuring the fact that diffusion is a general-purpose framework for learning continuous distributions, widely used in structural biology, audio synthesis, and robotics.

Genesis and Global Lineage

The core idea was formulated in 2015 by Jascha Sohl-Dickstein and colleagues at Stanford in Deep Unsupervised Learning using Nonequilibrium Thermodynamics (ICML 2015), drawing explicitly on the statistical physics of nonequilibrium processes: if forward diffusion destroys structure through a Markov chain of tiny Gaussian perturbations, the time-reversed process shares the same functional form and can be learned by a neural network. At the height of the Generative Adversarial Network (GAN) era inaugurated by Ian Goodfellow (2014), the paper attracted little notice because its generated samples looked blurry. The breakthrough arrived five years later along two converging paths. Yang Song and Stefano Ermon (2019) extended Aapo Hyvärinen’s statistical score matching (2005) into a generative method driven by Langevin dynamics, while Jonathan Ho, Ajay Jain, and Pieter Abbeel at UC Berkeley demonstrated in Denoising Diffusion Probabilistic Models (2020) that a simplified training objective—predicting the exact noise added at each step—produced images rivaling the best GANs. In 2021, Song, Sohl-Dickstein, and coauthors unified both lineages in the language of stochastic differential equations (SDEs). That same year Prafulla Dhariwal and Alexander Nichol at OpenAI declared that “diffusion models beat GANs on image synthesis,” and in 2022 Björn Ommer’s group in Munich moved the diffusion process into the compressed latent space of an autoencoder, creating Stable Diffusion and making high-resolution synthesis possible on a single consumer GPU. Since then, product marketing and media discourse have treated “diffusion” as shorthand for AI art, while research has evolved rapidly toward broader continuous-time families—flow matching, consistency models, and discrete diffusion—increasingly removed from the original thermodynamic metaphor.

Central European Lineage

We found no documented link between this concept and the intellectual history or historical experience of Central Europe.

Why Now

Between 2022 and 2024, diffusion ceased to be a conference algorithm and became cultural and scientific infrastructure. In April 2022 OpenAI unveiled DALL·E 2, followed by Google’s Imagen in May, and in August 2022 Stability AI released the open weights of Stable Diffusion, spawning within months a massive global ecosystem of community fine-tunes, LoRA adapters, and visual plugins. In January 2023 visual artists filed a class-action lawsuit against Stability AI, Midjourney, and DeviantArt, while Getty Images sued Stability AI in the United Kingdom (and in February 2023 in the United States), turning the question of scraped training data from an ethical debate into high-stakes copyright litigation. That same month, Nicholas Carlini’s team proved empirically that diffusion models memorize and regurgitate verbatim training images. In February 2024 OpenAI previewed its Sora video generator, built on a Diffusion Transformer (DiT) architecture, and in May 2024 Google DeepMind’s AlphaFold 3 replaced its earlier structural module with a diffusion module operating directly on atomic coordinates—demonstrating that the exact same mathematical machinery generates both commercial illustrations and biomolecular complexes. Simultaneously, the European Union’s AI Act (2024) introduced mandatory labeling and provenance obligations for synthetic content, aimed directly at the outputs of this class of models.

Explanatory Power

The concept reveals that “generative AI” actually encompasses two fundamentally different generative mechanisms with contrasting failure modes and economics. An autoregressive language model builds its output sequentially, token by token, inheriting every earlier commitment; a diffusion model refines the entire canvas simultaneously across dozens of passes, moving from coarse global composition to fine texture. This perspective explains three practical puzzles. First, it clarifies why image generators struggled for so long to render legible text or count five fingers on a hand: global layout crystallizes early at high noise levels, whereas rigid, discrete symbolic constraints are unnatural for a continuous local smoothing process. Second, it illuminates the distinct economics of visual inference: because generating a single sample requires running the neural network puluhan times in sequence, an entire sub-discipline (distillation, consistency models, fast ODE solvers) is essentially a battle to cut the number of denoising steps from fifty down to four or one. Third, it explains why diffusion excels at scientific inverse problems: reconstructing a sharp MRI scan from sparse sensor measurements or designing a protein backbone around a target binding site is literally conditional denoising—guiding a noisy trajectory toward the manifold of physically valid structures that satisfy an external constraint.

Axes of Debate

Underappreciated Angle

The least discussed property of diffusion models is that they never learn a probability distribution itself—only its local gradient (score). A diffusion model knows which direction from any noisy point leads toward “more probable” data, but it cannot state the absolute likelihood of a finished image, nor can it easily tell whether it is operating inside a densely supported region of the training data or extrapolating blindly into an empty corner of state space. Outside of art generation, this carries serious consequences: a diffusion model reconstructing a medical scan or proposing a novel molecular conformation produces outputs that look locally self-consistent and sharp by construction, yet has no native way to signal where its epistemic uncertainty is highest. A second overlooked implication concerns the role of random noise itself. Classical signal processing treated noise solely as an enemy to be filtered out; diffusion turns noise into the seed of variation, because it is the initial draw from a random number generator—not the user’s text prompt alone—that determines which specific image out of millions of prompt-compatible possibilities crystallizes. Authorship in diffusion systems is thus split three ways between the human (conditioning prompt), the model (learned score field), and the pseudorandom seed (trajectory selection)—a tripartite structure that copyright debates over AI-generated art have barely begun to address.