Uncanny Resemblances of Associative Memories and Diffusion Models

"The generative process of Diffusion Models (DMs) has recently set state-of-the-art on many AI generation benchmarks.

"Though the generative process is traditionally understood as an iterative denoiser, there is no universally accepted language to describe it. 

"We introduce a novel perspective to describe DMs using the mathematical language of memory retrieval from the field of energy-based Associative Memories (AMs), making efforts to keep our presentation approachable to newcomers to both of these fields. 

"Unifying these two fields provides insight that DMs can be seen as a particular kind of AM where Lyapunov stability guarantees are bypassed by intelligently engineering the dynamics (i.e., the noise and step size schedules) of the denoising process. 

"Finally, we present a growing body of evidence that records DMs exhibiting empirical behavior we would expect from AMs, and conclude by discussing research opportunities that are revealed by understanding DMs as a form of energy-based memory."

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