  Estimating and disentangling epistemic uncertainty (uncertainty that can be
reduced with more training data) and aleatoric uncertainty (uncertainty that is
inherent to the task at hand) is critically important when applying machine
learning (ML) to high-stakes applications such as medical imaging and weather
forecasting. Conditional diffusion models' breakthrough ability to accurately
and efficiently sample from the posterior distribution of a dataset now makes
uncertainty estimation conceptually straightforward: One need only train and
sample from a large ensemble of diffusion models. Unfortunately, training such
an ensemble becomes computationally intractable as the complexity of the model
architecture grows.
  In this work we introduce a new approach to ensembling, hyper-diffusion,
which allows one to accurately estimate epistemic and aleatoric uncertainty
with a single model. Unlike existing Monte Carlo dropout based single-model
ensembling methods, hyper-diffusion offers the same prediction accuracy as
multi-model ensembles. We validate our approach on two distinct tasks: x-ray
computed tomography (CT) reconstruction and weather temperature forecasting.
