  Multi-target detection (MTD) is the problem of estimating an image from a
large, noisy measurement that contains randomly translated and rotated copies
of the image. Motivated by the single-particle cryo-electron microscopy
technology, we design data-driven diffusion priors for the MTD problem, derived
from score-based stochastic differential equations models. We then integrate
the prior into the approximate expectation-maximization algorithm. In
particular, our method alternates between an expectation step that approximates
the expected log-likelihood and a maximization step that balances the
approximated log-likelihood with the learned log-prior. We show on two datasets
that adding the data-driven prior substantially reduces the estimation error,
in particular in high noise regimes.
