# Structure-based drug design by denoising voxel grids

arXiv: https://arxiv.org/abs/2405.03961 · HTML: https://mlsanity.com/paper/2405.03961/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 41 of its 75 references that are in the map.
- First posted on arXiv 7 May 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 41)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [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)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [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)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Are Transformers More Robust Than CNNs?](https://mlsanity.com/paper/2111.05464/) (2021)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [The Surprising Effectiveness of Diffusion Models for Optical Flow and Monocular Depth Estimation](https://mlsanity.com/paper/2306.01923/) (2023)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [ATOM3D: Tasks On Molecules in Three Dimensions](https://mlsanity.com/paper/2012.04035/) (2020)
- [Generating 3D Molecules Conditional on Receptor Binding Sites with Deep Generative Models](https://mlsanity.com/paper/2110.15200/) (2021)

## Built on by (most cited first, 19 of 19)

- [CBGBench: Fill in the Blank of Protein-Molecule Complex Binding Graph](https://mlsanity.com/paper/2406.10840/) (2024)
- [UniMoMo: Unified Generative Modeling of 3D Molecules for De Novo Binder Design](https://mlsanity.com/paper/2503.19300/) (2025)
- [Empower Structure-Based Molecule Optimization with Gradient Guided Bayesian Flow Networks](https://mlsanity.com/paper/2411.13280/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)
- [Unified all-atom molecule generation with neural fields](https://mlsanity.com/paper/2511.15906/) (2025)
- [Do we need equivariant models for molecule generation?](https://mlsanity.com/paper/2507.09753/) (2025)
- [Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transport](https://mlsanity.com/paper/2606.07239/) (2026)
- [IBEX: Information-Bottleneck-EXplored Coarse-to-Fine Molecular Generation under Limited Data](https://mlsanity.com/paper/2508.10775/) (2025)
- [Beyond Atoms: Evaluating Electron Density Representation for 3D Molecular Learning](https://mlsanity.com/paper/2511.21900/) (2025)
- [From Macro to Micro: Benchmarking Microscopic Spatial Intelligence on Molecules via Vision-Language Models](https://mlsanity.com/paper/2512.10867/) (2025)
- [MolSafeEval: A Benchmark for Uncovering Safety Risks in AI-Generated Molecules](https://mlsanity.com/paper/2607.00464/) (2026)
- [TransDiffSBDD: Causality-Aware Multi-Modal Structure-Based Drug Design](https://mlsanity.com/paper/2503.20913/) (2025)
- [MSCoD: An Enhanced Bayesian Updating Framework with Multi-Scale Information Bottleneck and Cooperative Attention for Structure-Based Drug Design](https://mlsanity.com/paper/2509.25225/) (2025)
- [SculptDrug : A Spatial Condition-Aware Bayesian Flow Model for Structure-based Drug Design](https://mlsanity.com/paper/2511.12489/) (2025)
- [Edge-aware GAT-based protein binding site prediction](https://mlsanity.com/paper/2601.02138/) (2026)
- [Multigrid Training for Molecular Generation using Graph Neural Networks](https://mlsanity.com/paper/2606.22377/) (2026)
- [Sesame: Structure-Aware Molecular Generation via Spatial Density-Map Conditioning](https://mlsanity.com/paper/2606.23856/) (2026)
- [A Systematic Evaluation of Molecule Generation Models for De Novo Drug Design: From Benchmarks to Practical Insights](https://mlsanity.com/paper/2609.10099/) (2026)
- [Blending experimental electron density information to protein-ligand interaction](https://mlsanity.com/paper/2610.14862/) (2026)

## Abstract (arXiv)

We present VoxBind, a new score-based generative model for 3D molecules conditioned on protein structures. Our approach represents molecules as 3D atomic density grids and leverages a 3D voxel-denoising network for learning and generation. We extend the neural empirical Bayes formalism (Saremi & Hyvarinen, 2019) to the conditional setting and generate structure-conditioned molecules with a two-step procedure: (i) sample noisy molecules from the Gaussian-smoothed conditional distribution with underdamped Langevin MCMC using the learned score function and (ii) estimate clean molecules from the noisy samples with single-step denoising. Compared to the current state of the art, our model is simpler to train, significantly faster to sample from, and achieves better results on extensive in silico benchmarks -- the generated molecules are more diverse, exhibit fewer steric clashes, and bind with higher affinity to protein pockets. The code is available at https://github.com/genentech/voxbind/.