# Unified Generative Modeling of 3D Molecules via Bayesian Flow Networks

arXiv: https://arxiv.org/abs/2403.15441 · HTML: https://mlsanity.com/paper/2403.15441/

## Key facts

- Cited by 18 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 24 of its 33 references that are in the map.
- First posted on arXiv 17 Mar 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, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [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)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generation](https://mlsanity.com/paper/2305.07508/) (2023)
- [Bayesian Flow Networks](https://mlsanity.com/paper/2308.07037/) (2023)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Learning to design drug-like molecules in three-dimensional space using deep generative models](https://mlsanity.com/paper/2104.08474/) (2021)
- [Generating 3D Molecular Structures Conditional on a Receptor Binding Site with Deep Generative Models](https://mlsanity.com/paper/2010.14442/) (2020)

## Built on by (most cited first, 18 of 18)

- [MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space](https://mlsanity.com/paper/2404.12141/) (2024)
- [CBGBench: Fill in the Blank of Protein-Molecule Complex Binding Graph](https://mlsanity.com/paper/2406.10840/) (2024)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [Applications of Modular Co-Design for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2505.18392/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [Empower Structure-Based Molecule Optimization with Gradient Guided Bayesian Flow Networks](https://mlsanity.com/paper/2411.13280/) (2024)
- [Piloting Structure-Based Drug Design via Modality-Specific Optimal Schedule](https://mlsanity.com/paper/2505.07286/) (2025)
- [Guiding Diffusion Models with Reinforcement Learning for Stable Molecule Generation](https://mlsanity.com/paper/2508.16521/) (2025)
- [Any-Property-Conditional Molecule Generation with Self-Criticism using Spanning Trees](https://mlsanity.com/paper/2407.09357/) (2024)
- [NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation](https://mlsanity.com/paper/2512.05844/) (2025)
- [Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fields](https://mlsanity.com/paper/2601.21985/) (2026)
- [RMFlow: Refined Mean Flow by a Noise-Injection Step for Multimodal Generation](https://mlsanity.com/paper/2602.00849/) (2026)
- [ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networks](https://mlsanity.com/paper/2405.15268/) (2024)
- [Tokenizing 3D Molecule Structure with Quantized Spherical Coordinates](https://mlsanity.com/paper/2412.01564/) (2024)
- [PhysicsGen: Can Generative Models Learn from Images to Predict Complex Physical Relations?](https://mlsanity.com/paper/2503.05333/) (2025)
- [Marked Temporal Bayesian Flow Point Processes](https://mlsanity.com/paper/2410.19512/) (2024)
- [A Systematic Evaluation of Molecule Generation Models for De Novo Drug Design: From Benchmarks to Practical Insights](https://mlsanity.com/paper/2609.10099/) (2026)
- [TreeRef-BFN: Equivariance-Free De Novo Molecule Generation based on 2D Topology and Internal 3D Geometry](https://mlsanity.com/paper/2609.32502/) (2026)

## Abstract (arXiv)

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the multi-modality and noise-sensitive nature of molecule geometry. This work introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits molecule geometry by modeling diverse modalities in the differentiable parameter space of distributions. GeoBFN maintains the SE-(3) invariant density modeling property by incorporating equivariant inter-dependency modeling on parameters of distributions and unifying the probabilistic modeling of different modalities. Through optimized training and sampling techniques, we demonstrate that GeoBFN achieves state-of-the-art performance on multiple 3D molecule generation benchmarks in terms of generation quality (90.87% molecule stability in QM9 and 85.6% atom stability in GEOM-DRUG. GeoBFN can also conduct sampling with any number of steps to reach an optimal trade-off between efficiency and quality (e.g., 20-times speedup without sacrificing performance).