MIST: Physics-Constrained Source–Transport Decomposition for Cryo-EM Heterogeneity

Learning interpretable latent structure from indirect observations is difficult when multiple mechanisms can explain the same measurements. Cryo-electron microscopy (cryo-EM) exhibits this ambiguity because an apparent structural change may arise from either motion of existing molecular density or local density gain and loss. Reconstruction error alone cannot determine which explanation is more appropriate. We introduce MIST (Mechanism-Informed Source–Transport), a Gaussian reconstruction model that structures the representation and training of the two mechanisms without requiring an accurate precomputed consensus reconstruction. Motion transports existing density with approximately mass-preserving deformation, while Source models local density changes and activates dormant anchors when variation extends beyond the canonical support. During joint training, a residual-guided coupled teacher estimates the local image responses of both mechanisms and provides coordinated update targets to reduce competition between them. After a reliable reconstruction has been established, a shared-density auxiliary objective encourages variation explainable by moving common density to be represented by Motion, while preserving the full reconstruction and the capacity of Source. Across synthetic and experimental cryo-EM datasets, MIST substantially reduces cross-mechanism leakage while maintaining high-fidelity heterogeneous reconstruction and producing clearer, more coherent structural details. These results demonstrate that mechanism-aware source–transport modeling improves mechanism attribution without compromising reconstruction fidelity.