研究问题与背景
We address the problem of learning generative priors over high-dimensional latent variables from indirect, noisy observations, with a focus on continuous heterogeneity in cryo-electron microscopy (cryo-EM). In this setting, 3D atomic structures $x \in \mathbb{R}^{3N_a}$ are never directly observed and must be inferred from 2D projection images $y$ generated by a complex, non-linear forward operator.
方法
Empirical Bayes Flow Matching (EB-FM)
We propose Empirical Bayes Flow Matching (EB-FM), a method that learns a flow matching prior $p_θ(x)$ directly from observations using a Monte Carlo stochastic approximation Expectation-Maximization framework.
E-step 与 M-step
EB-FM alternates between an E-step that performs approximate posterior sampling from $p_θ(x \mid y)$ via guided flow-based generation while maintaining persistent latent estimates through stochastic approximation, and an M-step that updates the flow model using these stabilized latent variables as training targets.
优势
This approach eliminates the need for pretraining on clean data and naturally accommodates non-linear forward models.
实验与验证
We validate our method on controlled inverse problems using two-moons and MNIST data, and demonstrate its effectiveness on simulated cryo-EM data with known poses, showing that EB-FM can recover continuous distributions of protein conformations directly in atomic-coordinate space.