Equivariant Diffusion for Molecule Generation in 3D

By Emiel Hoogeboom, Victor Garcia Satorras, Clément Vignac, Max Welling. 2022

962 citations recorded by the source corpus.

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time.

Subfields: Biophysics, Computational Theory and Mathematics, Materials Chemistry

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biophysics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

End-to-end protein–ligand complex structure generation with diffusion-based generative models (2022, methodology): “To ensure that the distributions are invariant to translation, we use distributions on the linear subspace [28] where the centroid of the molecular system is always at the origin and define Nx as a Gaussian distribution on this subspace, following [29].”
DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking (2022, methodology): “While DGMs have been applied to other problems in molecular machine learning [5, 6, 7], existing approaches are ill-suited for molecular docking, where the space of ligand poses is an ( m + 6) - dimensional submanifold M ⊂ R 3 n , where n and m are, respectively, the number of atoms and torsion…”
Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem (2022, positive): “Our resulting model, ProtDiff, is similar to concurrent work on E(3)-equivariant diffusion models for molecules [17], but with modifications specific to protein structure.”
Protein structure generation via folding diffusion (2022, methodology): “The E(3) Equivariant Diffusion Model (Hoogeboom et al., 2022) uses an equivariant transformer to design small molecules by diffusing on their coordinates in Euclidean space.”
DiGress: Discrete Denoising diffusion for graph generation (2022, methodology): “In this setting, we also measure atom stability and molecule stability as defined in (Hoogeboom et al., 2022).”
Structure-based drug design with equivariant diffusion models (2022, positive): “Generating compounds, or parts thereof, conditioned on a given molecular context is reminiscent of inpainting, a technique originally introduced for completing missing parts of images [37, 38] but also adopted in other domains, including biomolecular structures [39].”
TabDDPM: Modelling Tabular Data with Diffusion Models (2022, background): “, 2020b), molecular graphs (Jing et al., 2022; Hoogeboom et al., 2022), time series (Tashiro et al.”
DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models (2022, neutral): “…et al., 2021; Saharia et al., 2022b; Ramesh et al., 2022; Rombach et al., 2022; Gu et al., 2022), voice synthesis (Liu et al., 2022a; Chen et al., 2021a;b), molecule generation (Xu et al., 2022; Hoogeboom et al., 2022; Wu et al., 2022) and data compression (Theis et al., 2022; Kingma et al., 2021).”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, background): “Interdisciplinary Applications Molecular Graph Modeling [107],[94],[3],[259],[233], [247],[210],[152] Material Design [256],[153] Medical Image Reconstruction [224],[36],[37],[38],[178],[257]”
DiffusionDet: Diffusion Model for Object Detection (2022, background): “…models have recently demonstrated remarkable results in fields including computer vision [4,21,33,35,39,68,71,75,76,82,104,108], nature language processing [3,30,52], audio processing [41,48,50,70, 91,100,103], graph-related topics [42], interdisciplinary applications [2,40,44,78,94,99,102], etc.”
InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation (2023, background): “…Models Diffusion models [16, 17, 25, 26, 27, 28, 29, 30, 31] have achieved unprecedented results in various generative modeling tasks, including image/video generation [9, 32, 33, 34, 35], audio generation [36], point cloud generation [37, 38, 39, 40], biological generation [34, 41, 42, 43], etc..”
3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction (2023, background): “EDM (Hoogeboom et al., 2022) generates 3D molecules.”
DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization (2023, methodology): “We would also like to explore the use of equivariant graph neural networks [117, 45] for further improvement of the diffusion models on geometrical NP-complete combinatorial optimization problems such as Euclidean TSP. Finally, we are interested in utilizing (higher-order) accelerated inference…”
Building Normalizing Flows with Stochastic Interpolants (2022, neutral): “While this approach has shown great promise to model high dimensional distributions (Rombach et al., 2022; Hoogeboom et al., 2022), particularly in the case of text-to-image generation (Ramesh et al., 2022; Saharia et al., 2022), there is an absence of theoretical motivation for the SDE-ﬂow…”
Equivariant 3D-conditional diffusion model for molecular linker design (2022, neutral): “The molecule with the highest SC RDKit score, which captures the highest geometric and chemical similarity to the reference compound, is shown in Fig.”
Artificial intelligence in drug development (2025, neutral): “In contrast, non-autoregressive methods generate entire molecular graphs at once but need extra steps to ensure the graph’s validity, as these models’ limited perception of molecular topological structures can induce flawed structures 104 .”