  Uncovering the mechanisms behind long-term memory is one of the most
fascinating open problems in neuroscience and artificial intelligence.
Artificial associative memory networks have been used to formalize important
aspects of biological memory. Generative diffusion models are a type of
generative machine learning techniques that have shown great performance in
many tasks. Like associative memory systems, these networks define a dynamical
system that converges to a set of target states. In this work we show that
generative diffusion models can be interpreted as energy-based models and that,
when trained on discrete patterns, their energy function is (asymptotically)
identical to that of modern Hopfield networks. This equivalence allows us to
interpret the supervised training of diffusion models as a synaptic learning
process that encodes the associative dynamics of a modern Hopfield network in
the weight structure of a deep neural network. Leveraging this connection, we
formulate a generalized framework for understanding the formation of long-term
memory, where creative generation and memory recall can be seen as parts of a
unified continuum.
