Geometric Latent Diffusion Models for 3D Molecule Generation (2305.01140v1)

Abstract: 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 propose 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. Code is provided at \url{https://github.com/MinkaiXu/GeoLDM}.

• The paper introduces GeoLDM, a model that employs latent diffusion with invariant scalars and equivariant tensors to generate precise 3D molecular structures.
• It demonstrates significant improvements on QM9 and GEOM-DRUG datasets, achieving up to a 7% boost in molecule validity compared to existing methods.
• GeoLDM enables controllable generation by conditioning on chemical properties, paving the way for advancements in drug discovery and material science.

Overview of Geometric Latent Diffusion Models for 3D Molecule Generation

The paper, "Geometric Latent Diffusion Models for 3D Molecule Generation," presents a novel method for the generation of molecular geometries using latent diffusion models (LDMs). The primary contribution lies in the development of Geometric Latent Diffusion Models (GeoLDM), which operate in a latent space comprised of both invariant scalars and equivariant tensors to maintain roto-translational equivariance, which is essential for modeling 3D molecules.

Methodology

GeoLDM builds upon recent advancements in diffusion models (DMs) and extends them into the domain of 3D molecular geometry generation. The model is structured around autoencoders that map input geometries to a continuous latent space where the diffusion process is modeled. The key innovation is directly addressing the 3D geometric domain's roto-translational constraints by encoding these constraints within the latent space itself.

The paper introduces point-structured latent spaces consisting of both invariant and equivariant features, enabling the capture of complex molecular structures. The use of equivariant Graph Neural Networks (EGNNs) ensures that the transformations at every stage adhere to the required equivariances. This approach aims to reduce the dimensional complexity inherent in modeling atomic features directly and potentially enhances the generative model's expressiveness.

Results

Empirical results indicate that GeoLDM improves the quality of generated molecules, as evidenced by benchmarks on atom and molecule stability, validity, and uniqueness metrics. On the QM9 dataset, which features small molecules, and the GEOM-DRUG dataset, comprised of larger, more complex molecules, GeoLDM consistently outperforms state-of-the-art generative models like EDM and its variants. Notably, GeoLDM showed up to a 7% increase in the validity of large molecule generation, showcasing its enhanced capacity to model complex chemical spaces.

Additionally, the model exhibits improved controllable generation capabilities. Using polarizability and other quantum properties as conditions, GeoLDM demonstrates reduced Mean Absolute Errors in matching generated properties to target specifications when compared to baseline models. This demonstrates the model's ability to integrate desired properties into the molecular generation process.

Implications and Future Directions

GeoLDM sets a precedent for constructing generative models that can handle the inherent complexities of 3D molecular structures. The distinguishing feature of incorporating roto-translational symmetry in the latent space may inform future research on geometric generative models beyond molecular applications. The potential of GeoLDM to facilitate advancements in drug discovery, material science, and nanotechnology is substantial, particularly in scenarios requiring precise control over structural properties.

The paper also implicitly suggests several pathways for future research, such as scaling the model towards even larger molecular structures like proteins and exploring the application of this framework to other types of 3D geometric data. Additionally, further investigation into the optimization and stabilization of the latent space, especially concerning the balance between invariant and equivariant features, could yield further performance improvements.

Overall, the contribution of GeoLDM to 3D molecule generation delineates a path forward for leveraging latent diffusion models in geometry-sensitive domains, marking a significant step in the pursuit of more robust and flexible generative modeling frameworks in computational chemistry and beyond.