A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data
Reviewed by Pithpith:YSAKQENDopen to challenge →
read the original abstract
Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural networks capture during learning. Recent advancements show that diffusion models can generate high-quality images, hinting at their ability to capture this underlying compositional structure. We study this phenomenon in a hierarchical generative model of data. We find that the backward diffusion process acting after a time $t$ is governed by a phase transition at some threshold time, where the probability of reconstructing high-level features, like the class of an image, suddenly drops. Instead, the reconstruction of low-level features, such as specific details of an image, evolves smoothly across the whole diffusion process. This result implies that at times beyond the transition, the class has changed, but the generated sample may still be composed of low-level elements of the initial image. We validate these theoretical insights through numerical experiments on class-unconditional ImageNet diffusion models. Our analysis characterizes the relationship between time and scale in diffusion models and puts forward generative models as powerful tools to model combinatorial data properties.
This paper has not been read by Pith yet.
Forward citations
Cited by 5 Pith papers
-
Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
-
Quality-Preserving Imperceptible Adversarial Attack on Skeleton-based Human Action Recognition
A distribution-based adversarial attack generates quality-preserving adversarial motions for skeleton action recognition without noise perturbations, outperforming prior methods in success rate and naturalness on two ...
-
Local Diffusion Models and Phases of Data Distributions
The paper introduces a phase framework for data distributions connected by local denoisers and demonstrates that reverse diffusion consists of trivial and data phases separated by a transition where local score functi...
-
Statistical Properties of Training & Generalization
Neural scaling laws in deep learning interact with physics constraints and inductive biases beyond classical statistics.
-
Statistical Properties of Training & Generalization
Review of neural scaling laws and their relation to constraints and inductive biases when applying machine learning to physics problems.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.