Cryo-SWAN: the Multi-Scale Wavelet-decomposition-inspired Autoencoder Network for molecular density representation of molecular volumes
Authors: Rui Li, Artsemi Yushkevich, Mikhail Kudryashev, Artur Yakimovich
Organizations: Center for Advanced Systems Understanding (CASUS), Görlitz, Germany. · Helmholtz-Zentrum Dresden-Rossendorf e. V. (HZDR), Dresden, Germany. · In situ Structural Biology, Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany. · Department of Physics, Humboldt University of Berlin, Berlin, Germany. · Institute of Medical Physics and Biophysics, Charite-Universitätsmedizin, Berlin, Germany. · Institute of Computer Science, University of Wrocaw, Wrocaw, Poland. · Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany.
Learning robust representations of 3D shapes from voxelized data is essential for advancing AI methods in biomedical imaging. However, most contemporary 3D computer vision approaches operate on point clouds, meshes, or octrees, while volumetric density maps, the native format of structural biology and cryo-EM, remain comparatively underexplored. We present Cryo-SWAN, a voxel-based variational autoencoder inspired by multi-scale wavelet decomposition. The model performs conditional coarse-to-fine latent encoding and recursive residual quantization across perception scales, enabling accurate capture of both global geometry and high-frequency structural detail in molecular density volumes. Evaluated on ModelNet40, BuildingNet, and a newly curated dataset of cryo-EM volumes, ProteinNet3D, Cryo-SWAN consistently improves reconstruction quality over state-of-the-art 3D autoencoders. We demonstrate that the molecular densities organize in learned latent space according to shared geometric features, while integration with diffusion models enables denoising and conditional shape generation. Together, Cryo-SWAN is a practical framework for data-driven structural biology and volumetric imaging.
Figures & tables
Figure 1: Principle architecture of Multi-Scale Wavelet-decomposition-inspired Autoencoder Network . (a) Multi-scale decomposition of the input signal. (b) The residual quantization process. A residual loss is computed during codebook lookup at each scale. (c) Downstream applications of the voxel-based 3D shape representations.
Figure 2: cryo-SWAN performance on common 3D shape benchmarks . (a) Performance on three representative objects from BuildingNet dataset. (b) Performance on three representative objects from ModelNet dataset. Here, low, mix, and high denote the frequency components, where mix captures a combination of low- and high-frequency details.
Figure 3: Representation learning on the ProteinNet3D and explorations in the latent space. (a) The representation learning on the ProteinNet3D. (b) The FSC evaluation of all the representations. (c) Dimensionality reduction comparison: Cryo-SWAN latent vectors vs. original EMDB volumes. (d) UMAP projection of latent vectors reveals distinct hubs reflecting structural similarity. Molecules with similar 3D structures at 8 Å resolution (siblings).
Figure 4: Ablation study for codebook collapsing and multi-scale representations. (a) The calls for all the codebook entries. (b) The latent code representation for both scales (coarse and fine). (c) The molecular density volume: original (GT), at a certain representation scale (RQ1) and at a full representation (RQ1+RQ2). (d) Evaluation of representation performance at a certain representation scale (RQ1) compared to the full representation (RQ1+RQ2).
Figure 5: Downstream applications of cryo-SWAN including shape denoising and conditional molecular shape generation. (a) The conditional generation from diffusion models based on cryo-SWAN representations. (b) Examples of conditional generations. The variants are similar in the geometric perspective to the real protein densities in EMDB (anchor point). (c) The unsupervised denoising based on the representation learning for 3D densities from ModelNet.
Figure S1 : Optimal choice of the pixel size and the volume size. (top) Volume size distribution at various resampled pixel size. (bottom) Volumes distribution respective to the originally reported resolution and the pixel size: ProteinNet3D volumes, preserving original resolution after resampling (blue) and degraded to 8A˚ after resampling due to the Nyquist limit (green), as well as filtered out volumes due to the cutoffs applied (white).
Figure S3 : ProteinNet3D complexity: membrane-related signal and experimental noise presence. (top) Normal protein densities in ProteinNet. (middle) ProteinNet example volumes containing membrane-related signal. (bottom) ProteinNet example volumes containing experimental noise
Figure S4 : Molecular shapes similarity within hubs identified with Cryo-SWAN.
Figure S5 : The latent diffusion generation based on cryo-SWAN representation.
Scientific user facilities generate X-ray scattering data faster than traditional workflows can process them. We address this challenge across two settings, offline dataset exploration and live on-the-fly analysis. We train a domain-specific attention-based Convolutional Variational Autoencoder (C-VAE) on 1.5 million X-ray scattering images to learn low-dimensional representations capturing structural variation across diverse experimental conditions. The learned latent space reveals well-organized clusters and smooth trajectories reflecting experimental progression. It further supports controlled synthetic scattering image generation across diverse structural states. When deployed without retraining, the model organizes time-resolved film formation experiments at two synchrotron facilities into interpretable latent structures. Benchmarking against DINOv3 (ViT-7B), a general-purpose vision foundation model, demonstrates that domain-specific training yields more interpretable latent organization for scattering data. Both workflows are integrated within Latent Space Explorer, a component of the MLExchange platform, supporting interactive structural exploration across archived datasets and live experiments.
Monika Choudhary, Xiaoya Chong, Runbo Jiang +25
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA · Center for Advanced Mathematics for Energy Research Applications, Lawrence Berkeley National Laboratory, Berkeley, CA, USA · Molecular Biophysics & Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA +9
CryoEM map interpretation requires features that are spatially localized, consistent across samples, and informative across spatial scales. Most deep learning methods for map annotation extract features from fixed voxel grids. However, implicit neural representations (INRs) are able to model volumetric data as scale-agnostic, coordinate-conditioned functions. INRs are therefore attractive for cryoEM, but fitting a separate INR for each map is too expensive for large-scale feature extraction and produces representations that are not aligned across samples. We introduce Atelier, a self-supervised framework that amortizes INR fitting for reconstructed cryoEM maps. Pretrained on 5,439 Electron Microscopy Data Bank maps, Atelier is a transformer-based hypernetwork that generates high-fidelity reconstructions across a wide range of protein structures, including large multi-subunit assemblies. Beyond reconstruction, the INR generated by the pretrained transformer exposes a continuous, local feature field through its intermediate activations at any spatial query point, a property that voxel grid and patch-tokenizer architectures do not naturally provide. Used as auxiliary channels to a 3D nested U-Net annotation head trained from scratch, these coordinate-conditioned features improve performance on eight voxel-level property prediction tasks over a volume-only baseline. Our results demonstrate that amortized implicit neural representations are an effective primitive for geometry-aware analysis of cryoEM data.
Phillip Lo, Sudarshan Babu, Dari Kimanius +1
Biohub Chicago, IL · University of Chicago, Biohub Chicago, IL
Self-supervised learning in fluorescence microscopy often relies on 2D projections, despite the inherently three-dimensional nature of cells. We present a systematic comparison of 2D and 3D masked autoencoders (MAE-2D vs. MAE-3D) on volumetric microscopy data. Under matched architectures and training protocols, MAE-3D consistently outperforms 2D max-projection and slice-based variants on downstream single-cell tasks. We further align visual representations with a pretrained protein language model (ESM2) and show that cross-modal supervision yields larger gains for volumetric models. Channel cross-attention and frequency-domain regularization are critical for leveraging 3D spatial context. On protein--protein interaction prediction, our best model achieves a ROC--AUC of 0.86, while on protein localization it reaches an AUCmicro of 0.95 and an F1micro of 0.74, demonstrating competitive performance on both tasks. Overall, our findings highlight the potential of volumetric modeling and multimodal alignment for representation learning in single-cell microscopy.
Institute of AI for Health & Helmholtz AI, Computational Health Center, Helmholtz Munich – German Research Center for Environmental Health, Neuherberg, Germany · Munich Center for Machine Learning (MCML), Munich, Germany · Department of Medicine III, Ludwig-Maximilian-University Hospital, Munich, Germany +2