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Diffusion Models (DMs) have recently set state-of-the-art on many generationbenchmarks. However, there are myriad ways to describe them mathematically,which makes it difficult to develop a simple understanding of how they work. Inthis survey, we provide a concise overview of DMs from the perspective ofdynamical systems and Ordinary Differential Equations (ODEs) which exposes amathematical connection to the highly related yet often overlooked class ofenergy-based models, called Associative Memories (AMs). Energy-based AMs are atheoretical framework that behave much like denoising DMs, but they enable usto directly compute a Lyapunov energy function on which we can perform gradientdescent to denoise data. We then summarize the 40 year history of energy-basedAMs, beginning with the original Hopfield Network, and discuss new researchdirections for AMs and DMs that are revealed by characterizing the extent oftheir similarities and differences

Memory in Plain Sight: A Survey of the Uncanny Resemblances between Diffusion Models and Associative Memories