Probing the Latent Hierarchical Structure of Data via Diffusion Models

TL;DR

This paper demonstrates that diffusion models can be used to probe and measure the hierarchical latent structure of data, revealing how data changes relate to underlying latent variables.

Contribution

It introduces a novel method using forward-backward diffusion experiments to analyze the latent hierarchical structure in high-dimensional data.

Findings

Latent variable changes manifest as correlated chunks in data.

A phase transition in the noise level indicates a change in data structure.

Validated approach on text and image datasets with state-of-the-art diffusion models.

Abstract

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce. Likewise, accessing the latent variables underlying such a data structure remains a challenge. In this work, we show that forward-backward experiments in diffusion-based models, where data is noised and then denoised to generate new samples, are a promising tool to probe the latent structure of data. We predict in simple hierarchical models that, in this process, changes in data occur by correlated chunks, with a length scale that diverges at a noise level where a phase transition is known to take place. Remarkably, we confirm this prediction in both text and image datasets using state-of-the-art diffusion models. Our results show how latent variable changes manifest in the data and establish how to measure these effects in real data using diffusion models.