Probing the Latent Hierarchical Structure of Data via Diffusion Models
This work addresses the challenge of probing latent variables in data structure for researchers in machine learning and data analysis, though it is incremental as it builds on existing diffusion model frameworks.
The paper tackled the problem of quantitatively measuring the latent hierarchical structure of high-dimensional data, showing that forward-backward experiments in diffusion models reveal correlated changes in data chunks, with predictions confirmed on text and image datasets using state-of-the-art models.
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.