---
title: "Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.05202v1"
permalink: "https://feed.astralor.com/items/itm_b582ee9b48a9b92abb8c2066"
published: "2026-11-03T16:51:30.000Z"
score: 59
channel: "tech"
tags: ["Empirical Bayes Flow","Matching","Continuous Cryo-EM Heterogeneity","EB-FM","Monte Carlo","Expectation-Maximization"]
---

# Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity

## At a glance

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 sett…

## Key points

- 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.
- 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.

## Full text

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. 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 $p_θ(x \mid y)$ 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. 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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