# 3D molecule generation by denoising voxel grids

arXiv: https://arxiv.org/abs/2306.07473 · HTML: https://mlsanity.com/paper/2306.07473/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 98 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 30 of 65)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)

## Built on by (most cited first, 30 of 40)

- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [RGFN: Synthesizable Molecular Generation Using GFlowNets](https://mlsanity.com/paper/2406.08506/) (2024)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)
- [CBGBench: Fill in the Blank of Protein-Molecule Complex Binding Graph](https://mlsanity.com/paper/2406.10840/) (2024)
- [Applications of Modular Co-Design for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2505.18392/) (2025)
- [Equivariant Neural Diffusion for Molecule Generation](https://mlsanity.com/paper/2506.10532/) (2025)
- [3D Vessel Graph Generation Using Denoising Diffusion](https://mlsanity.com/paper/2407.05842/) (2024)
- [Unified Cross-Scale 3D Generation and Understanding via Autoregressive Modeling](https://mlsanity.com/paper/2503.16278/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [E(3)-equivariant models cannot learn chirality: Field-based molecular generation](https://mlsanity.com/paper/2402.15864/) (2024)
- [Tactile DreamFusion: Exploiting Tactile Sensing for 3D Generation](https://mlsanity.com/paper/2412.06785/) (2024)
- [Molecular Representations in Implicit Functional Space via Hyper-Networks](https://mlsanity.com/paper/2601.22327/) (2026)
- [Cell Morphology-Guided Small Molecule Generation with GFlowNets](https://mlsanity.com/paper/2408.05196/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)
- [ProxelGen: Generating Proteins as 3D Densities](https://mlsanity.com/paper/2506.19820/) (2025)
- [NEBULA: Neural Empirical Bayes Under Latent Representations for Efficient and Controllable Design of Molecular Libraries](https://mlsanity.com/paper/2407.03428/) (2024)
- [A noise-corrected Langevin algorithm and sampling by half-denoising](https://mlsanity.com/paper/2410.05837/) (2024)
- [Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Space](https://mlsanity.com/paper/2506.00771/) (2025)
- [Unraveling the Potential of Diffusion Models in Small Molecule Generation](https://mlsanity.com/paper/2507.08005/) (2025)
- [Unified all-atom molecule generation with neural fields](https://mlsanity.com/paper/2511.15906/) (2025)
- [3D Molecule Generation from Rigid Motifs via SE(3) Flows](https://mlsanity.com/paper/2601.16955/) (2026)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [nach0-pc: Multi-task Language Model with Molecular Point Cloud Encoder](https://mlsanity.com/paper/2410.09240/) (2024)
- [Do we need equivariant models for molecule generation?](https://mlsanity.com/paper/2507.09753/) (2025)
- [Controllable 3D Molecular Generation for Structure-Based Drug Design Through Bayesian Flow Networks and Gradient Integration](https://mlsanity.com/paper/2508.21468/) (2025)
- [Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transport](https://mlsanity.com/paper/2606.07239/) (2026)
- [Grand canonical generative diffusion model for crystalline phases and grain boundaries](https://mlsanity.com/paper/2408.15601/) (2024)
- [Beyond Atoms: Evaluating Electron Density Representation for 3D Molecular Learning](https://mlsanity.com/paper/2511.21900/) (2025)
- [Training Dynamics of Learning 3D-Rotational Equivariance](https://mlsanity.com/paper/2512.02303/) (2025)

## Abstract (arXiv)

We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution of real molecules. Then, we follow the neural empirical Bayes framework (Saremi and Hyvarinen, 19) and generate molecules in two steps: (i) sample noisy density grids from a smooth distribution via underdamped Langevin Markov chain Monte Carlo, and (ii) recover the "clean" molecule by denoising the noisy grid with a single step. Our method, VoxMol, generates molecules in a fundamentally different way than the current state of the art (ie, diffusion models applied to atom point clouds). It differs in terms of the data representation, the noise model, the network architecture and the generative modeling algorithm. Our experiments show that VoxMol captures the distribution of drug-like molecules better than state of the art, while being faster to generate samples.