# Cryo-SWAN: the Multi-Scale Wavelet-decomposition-inspired Autoencoder Network for molecular density representation of molecular volumes

arXiv: https://arxiv.org/abs/2603.03342 · HTML: https://mlsanity.com/paper/2603.03342/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 27 of 27)

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- [BCR-Net: a neural network based on the nonstandard wavelet form](https://mlsanity.com/paper/1810.08754/) (2018)
- [ViT-AE++: Improving Vision Transformer Autoencoder for Self-supervised Medical Image Representations](https://mlsanity.com/paper/2301.07382/) (2023)
- [Unsupervised Object Representation Learning using Translation and Rotation Group Equivariant VAE](https://mlsanity.com/paper/2210.12918/) (2022)
- [A Deep Learning Method for Simultaneous Denoising and Missing Wedge Reconstruction in Cryogenic Electron Tomography](https://mlsanity.com/paper/2311.05539/) (2023)
- [Solving the inverse problem of microscopy deconvolution with a residual Beylkin-Coifman-Rokhlin neural network](https://mlsanity.com/paper/2407.03239/) (2024)

## Abstract (arXiv)

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.