# Distributional Priors Guided Diffusion for Generating 3D Molecules in Low Data Regimes

arXiv: https://arxiv.org/abs/2404.00962 · HTML: https://mlsanity.com/paper/2404.00962/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 1 Apr 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, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (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)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [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)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Hit and Lead Discovery with Explorative RL and Fragment-based Molecule Generation](https://mlsanity.com/paper/2110.01219/) (2021)
- [MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generation](https://mlsanity.com/paper/2305.07508/) (2023)
- [Learning Invariant Molecular Representation in Latent Discrete Space](https://mlsanity.com/paper/2310.14170/) (2023)
- [t-SMILES: A Scalable Fragment-based Molecular Representation Framework for De Novo Molecule Generation](https://mlsanity.com/paper/2301.01829/) (2023)

## Abstract (arXiv)

Can we train a 3D molecule generator using data from dense regions to generate samples in sparse regions? This challenge can be framed as an out-of-distribution (OOD) generation problem. While prior research on OOD generation predominantly targets property shifts, structural shifts -- such as differences in molecular scaffolds or functional groups -- represent an equally critical source of distributional shifts. This work introduces the Geometric OOD Diffusion Model (GODD), a novel diffusion-based framework that enables training on data-abundant molecular distributions while generalizing to data-scarce distributions under distributional structural shifts. Central to our approach is a designated equivariant asymmetric autoencoder to capture distributional structural priors. The asymmetric design allows the model to generalize to unseen structural variations by capturing distributional priors representing distinct distributions. The encoded structural-grained priors guide generation toward sparse regions without requiring explicit training on such data. Evaluated across standard benchmarks encompassing OOD structural shifts (e.g., scaffolds, rings), GODD achieves an improvement of 12.6% in success rate, defined based on molecular validity, uniqueness, and novelty. Furthermore, the framework demonstrates promising performance and generalization on canonical fragment-based drug design tasks, highlighting its utility in learning-based molecular discovery.