HeteroGauss: Heterogeneity-Aware Gaussian Representation for Cryo-EM Reconstruction

Single-particle cryo-EM captures biomolecular structures with continuous conformational and discrete compositional variability, yet each particle image is an extremely noisy 2D projection of one unknown state. Recovering heterogeneous ensembles requires sharing information across particles while preserving structural correspondence, allowing molecular elements to move, appear or disappear, and adapt spatial capacity to unresolved heterogeneous regions. Existing voxel, implicit-field, and deformation-based models typically satisfy only part of these requirements, either lacking explicit cross-state correspondence, relying on an established reference, or retaining fixed spatial support throughout reconstruction. We propose HeteroGauss, a shared, state-conditioned anisotropic Gaussian representation for heterogeneous cryo-EM reconstruction. Mechanistically, each Gaussian preserves identity across molecular states while its position, scale, orientation, and amplitude vary with the inferred latent state, enabling explicit modeling of both conformational and compositional variability. Learnable spatial anchors coordinate local deformation, while a heterogeneity-aware adaptive topology mechanism reallocates primitives using reconstruction gradients and state-dependent motion. Technically, a batched differentiable CUDA renderer enables efficient optimization of particle-specific Gaussian structures. Experiments on CryoBench and EMPIAR-10180 show that HeteroGauss reconstructs continuous and compositional heterogeneity with strong accuracy and retains substantially more reproducible high-frequency detail on experimental data. Codes are attached for evaluation. Project Webpage.