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Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we proposed a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM’s higher capacity for controllable generation thanks to the latent modeling. 

How enzymes achieve their enormous rate enhancements remains a central question in biology, and our understanding to date has impacted drug development, influenced enzyme design, and deepened our appreciation of evolutionary processes. While enzymes position catalytic and reactant groups in active sites, physics requires that atoms undergo constant motion. Numerous proposals have invoked positioning or motions as central for enzyme function, but a scarcity of experimental data has limited our understanding of positioning and motion, their relative importance, and their changes through the enzyme’s reaction cycle. To examine positioning and motions and test catalytic proposals, we collected “room temperature” X-ray crystallography data forPseudomonas putidaketosteroid isomerase (KSI), and we obtained conformational ensembles for this and a homologous KSI from multiple PDB crystal structures. Ensemble analyses indicated limited change through KSI’s reaction cycle. Active site positioning was on the 1- to 1.5-Å scale, and was not exceptional compared to noncatalytic groups. The KSI ensembles provided evidence against catalytic proposals invoking oxyanion hole geometric discrimination between the ground state and transition state or highly precise general base positioning. Instead, increasing or decreasing positioning of KSI’s general base reduced catalysis, suggesting optimized Ångstrom-scale conformational heterogeneity that allows KSI to efficiently catalyze multiple reaction steps. Ensemble analyses of surrounding groups for WT and mutant KSIs provided insights into the forces and interactions that allow and limit active-site motions. Most generally, this ensemble perspective extends traditional structure–function relationships, providing the basis for a new era of “ensemble–function” interrogation of enzymes.