An analytic theory of creativity in convolutional diffusion models
Journal:
arXiv
Published Date:
Dec 28, 2024
Abstract
We obtain the first analytic, interpretable and predictive theory of
creativity in convolutional diffusion models. Indeed, score-based diffusion
models can generate highly creative images that lie far from their training
data. But optimal score-matching theory suggests that these models should only
be able to produce memorized training examples. To reconcile this
theory-experiment gap, we identify two simple inductive biases, locality and
equivariance, that: (1) induce a form of combinatorial creativity by preventing
optimal score-matching; (2) result in a fully analytic, completely
mechanistically interpretable, equivariant local score (ELS) machine that, (3)
without any training can quantitatively predict the outputs of trained
convolution only diffusion models (like ResNets and UNets) with high accuracy
(median $r^2$ of $0.90, 0.91, 0.94$ on CIFAR10, FashionMNIST, and MNIST). Our
ELS machine reveals a locally consistent patch mosaic model of creativity, in
which diffusion models create exponentially many novel images by mixing and
matching different local training set patches in different image locations. Our
theory also partially predicts the outputs of pre-trained self-attention
enabled UNets (median $r^2 \sim 0.75$ on CIFAR10), revealing an intriguing role
for attention in carving out semantic coherence from local patch mosaics.
