Diffusion Models and Concept Formation
Paper argues diffusion models implicitly form Cobweb-like concept hierarchies, with a basic level emerging at intermediate noise levels.
The authors draw a formal correspondence between diffusion models and Cobweb, a classic incremental concept-hierarchy learner, noting both are hierarchical Bayesian density models with Gaussian prototypes. Modes of the diffusion model's noisy marginals form a hierarchy whose basic level sits at intermediate noise, where class identity commits. The correspondence is tested on MNIST and Fashion-MNIST via mode-finding. Diffusion is reframed as a cognitive model of concept formation.
- Noisy marginals of diffusion models mirror Cobweb probabilistic prototype trees
- Basic level of categorization emerges at intermediate noise levels
- Correspondence validated on MNIST and Fashion-MNIST via mode-finding
Full article238 words · extracted from arxiv.org · click to collapse
Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.13047