Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity
Abstract
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 ∈ ℝ3Na are never directly observed and must be inferred from 2D projection images y generated by a complex, non-linear forward operator. We propose Empirical Bayes Flow Matching (EB-FM), a method that learns a flow matching prior pθ(x) directly from observations using a Monte Carlo stochastic approximation Expectation-Maximization framework. EB-FM alternates between an E-step that performs approximate posterior sampling from pθ(x | 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. This approach eliminates the need for pretraining on clean data and naturally accommodates non-linear forward models. 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.
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BibTeX
@misc{aibinder2026empirical,
title = {{Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity}},
author = {Daniel Aibinder and Azmi Haider and Dan Rosenbaum},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05202},
eprint = {2611.05202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05202},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity
AU - Daniel Aibinder
AU - Azmi Haider
AU - Dan Rosenbaum
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05202
UR - https://arxiv.org/abs/2611.05202
AB - 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 ∈ ℝ^3N_a are never directly observed and must be inferred from 2D projection images y generated by a complex, non-linear forward operator. 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. EB-FM alternates between an E-step that performs approximate posterior sampling from p_θ(x | 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. This approach eliminates the need for pretraining on clean data and naturally accommodates non-linear forward models. 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.
ER -