mlsanityData to 14 Oct 2026

Latent Space Diffusion Models of Cryo-EM Structures

arXiv 2211.14169 ↗First posted 25 Nov 2022q-bio.QM stat.MLcited by 6

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Cryo-electron microscopy (cryo-EM) is unique among tools in structural biology in its ability to image large, dynamic protein complexes. Key to this ability is image processing algorithms for heterogeneous cryo-EM reconstruction, including recent deep learning-based approaches. The state-of-the-art method cryoDRGN uses a Variational Autoencoder (VAE) framework to learn a continuous distribution of protein structures from single particle cryo-EM imaging data. While cryoDRGN can model complex structural motions, the Gaussian prior distribution of the VAE fails to match the aggregate approximate posterior, which prevents generative sampling of structures especially for multi-modal distributions (e.g. compositional heterogeneity). Here, we train a diffusion model as an expressive, learnable prior in the cryoDRGN framework. Our approach learns a high-quality generative model over molecular conformations directly from cryo-EM imaging data. We show the ability to sample from the model on two synthetic and two real datasets, where samples accurately follow the data distribution unlike samples from the VAE prior distribution. We also demonstrate how the diffusion model prior can be leveraged for fast latent space traversal and interpolation between states of interest. By learning an accurate model of the data distribution, our method unlocks tools in generative modeling, sampling, and distribution analysis for heterogeneous cryo-EM ensembles.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 42 of its 67 references that are in the map. First posted on arXiv 25 Nov 2022.

Builds on

42 of 67 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  2. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models26 May
  3. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  4. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  5. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb

Other references · 37

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  7. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  8. 2022Classifier-Free Diffusion Guidancecited by 5,847
  9. 2013Auto-Encoding Variational Bayescited by 4,053
  10. 2018Neural Ordinary Differential Equationscited by 3,779
  11. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  12. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
25 more
  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  2. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  3. 2021Palette: Image-to-Image Diffusion Modelscited by 1,300
  4. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  5. 2021Score-based Generative Modeling in Latent Spacecited by 636
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  7. 2021Neural Fields in Visual Computing and Beyondcited by 540
  8. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 516
  9. 2021Diffusion Autoencoders: Toward a Meaningful and Decodable Representationcited by 449
  10. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 264
  11. 2022Torsional Diffusion for Molecular Conformer Generationcited by 263
  12. 2017VAE with a VampPriorcited by 248
  13. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 233
  14. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 163
  15. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 106
  16. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 104
  17. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latentscited by 104
  18. 2019NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transportcited by 74
  19. 2018Resampled Priors for Variational Autoencoderscited by 57
  20. 2019Reconstructing continuous distributions of 3D protein structure from cryo-EM imagescited by 56
  21. 2018Distribution Matching in Variational Inferencecited by 35
  22. 2018Variational Autoencoder with Implicit Optimal Priorscited by 33
  23. 2022Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopycited by 19
  24. 2021Inferring a Continuous Distribution of Atom Coordinates from Cryo-EM Images using VAEscited by 17
  25. 2019All SMILES Variational Autoencodercited by 15

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Citing papers per year: 2023: 2; 2024: 3; 2025: 1.

6 papers.

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  1. 2026Cryo-SWAN: the Multi-Scale Wavelet-decomposition-inspired Autoencoder Network for molecular density representation of molecular volumes
  2. 2025CryoCCD: Conditional Cycle-consistent Diffusion with Biophysical Modeling for Cryo-EM Synthesis
  3. 2025cryoSENSE: Compressive Sensing Enables High-throughput Microscopy with Sparse and Generative Priors on the Protein Cryo-EM Image Manifold
  4. 2026CryoNet.Refine: A One-step Diffusion Model for Rapid Refinement of Structural Models with Cryo-EM Density Map Restraints
  5. 2026Latent Diffusion Pretraining for Crystal Property Prediction
  6. 2025SemiETPicker: Fast and Label-Efficient Particle Picking for CryoET Tomography Using Semi-Supervised Learning
  7. 2024Robust single-particle cryo-EM image denoising and restoration
  8. 2025Compressing Biology: Evaluating the Stable Diffusion VAE for Phenotypic Drug Discovery