How Diffusion Models Learn to Factorize and Compose

Abstract

Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Inspired by cognitive neuroscientific approaches, we consider a highly reduced setting to examine whether and when diffusion models learn semantically meaningful and factorized representations of composable features. We performed extensive controlled experiments on conditional Denoising Diffusion Probabilistic Models (DDPMs) trained to generate various forms of 2D Gaussian data. We found that the models learn factorized but not fully continuous manifold representations for encoding continuous features of variation underlying the data. With such representations, models demonstrate superior feature compositionality but limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with few compositional examples, suggesting a more efficient way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, offering insight into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data.

Qiyao (Catherine) Liang

PhD student at MIT EECS

I’m a third-year PhD student in the Electrical Engineering and Computer Science department at MIT. My primary interest is in the intersection of physics, AI, and neuroscience. I’m advised by Ila Fiete from the MIT Brain and Cognitive Science department. Some of my recent interests are understanding the mechanisms of compositional generalization in generative models, how structural and/or functional modularity emerge within artificial and biological systems, and beyond. I’m interested in a broad range of topics regarding studying the principles of artificial/biological intelligence and consciousness as emergent phenomena, via quantitative tools from physics as well as empirical studies. I completed my undergraduate studies at Duke University in physics and math, where I worked on controlling and denoising quantum computers.