# NEBULA: Neural Empirical Bayes Under Latent Representations for Efficient and Controllable Design of Molecular Libraries

arXiv: https://arxiv.org/abs/2407.03428 · HTML: https://mlsanity.com/paper/2407.03428/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 26 of 26)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [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)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Neural Empirical Bayes](https://mlsanity.com/paper/1903.02334/) (2019)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Application of generative autoencoder in de novo molecular design](https://mlsanity.com/paper/1711.07839/) (2017)
- [Learning a Continuous Representation of 3D Molecular Structures with Deep Generative Models](https://mlsanity.com/paper/2010.08687/) (2020)
- [PubChemQC B3LYP/6-31G*//PM6 dataset: the Electronic Structures of 86 Million Molecules using B3LYP/6-31G* calculations](https://mlsanity.com/paper/2305.18454/) (2023)
- [Multimeasurement Generative Models](https://mlsanity.com/paper/2112.09822/) (2021)
- [Autoregressive fragment-based diffusion for pocket-aware ligand design](https://mlsanity.com/paper/2401.05370/) (2023)
- [Universal Smoothed Score Functions for Generative Modeling](https://mlsanity.com/paper/2303.11669/) (2023)
- [SupSiam: Non-contrastive Auxiliary Loss for Learning from Molecular Conformers](https://mlsanity.com/paper/2302.07754/) (2023)
- [Rethinking U-net Skip Connections for Biomedical Image Segmentation](https://mlsanity.com/paper/2402.08276/) (2024)
- [Soft Random Sampling: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2311.12727/) (2023)

## Built on by (most cited first, 3 of 3)

- [Do we need equivariant models for molecule generation?](https://mlsanity.com/paper/2507.09753/) (2025)
- [Pesti-Gen: Unleashing a Generative Molecule Approach for Toxicity Aware Pesticide Design](https://mlsanity.com/paper/2501.14469/) (2025)
- [Training Dynamics of Learning 3D-Rotational Equivariance](https://mlsanity.com/paper/2512.02303/) (2025)

## Abstract (arXiv)

We present NEBULA, the first latent 3D generative model for scalable generation of large molecular libraries around a seed compound of interest. Such libraries are crucial for scientific discovery, but it remains challenging to generate large numbers of high quality samples efficiently. 3D-voxel-based methods have recently shown great promise for generating high quality samples de novo from random noise (Pinheiro et al., 2023). However, sampling in 3D-voxel space is computationally expensive and use in library generation is prohibitively slow. Here, we instead perform neural empirical Bayes sampling (Saremi & Hyvarinen, 2019) in the learned latent space of a vector-quantized variational autoencoder. NEBULA generates large molecular libraries nearly an order of magnitude faster than existing methods without sacrificing sample quality. Moreover, NEBULA generalizes better to unseen drug-like molecules, as demonstrated on two public datasets and multiple recently released drugs. We expect the approach herein to be highly enabling for machine learning-based drug discovery. The code is available at https://github.com/prescient-design/nebula