# Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D

arXiv: https://arxiv.org/abs/2305.13266 · HTML: https://mlsanity.com/paper/2305.13266/

## Key facts

- Cited by 24 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 44 of its 65 references that are in the map.
- First posted on arXiv 5 May 2023.

## 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 44)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [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)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [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)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Generalization in Generation: A closer look at Exposure Bias](https://mlsanity.com/paper/1910.00292/) (2019)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)

## Built on by (most cited first, 24 of 24)

- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Equivariant Neural Diffusion for Molecule Generation](https://mlsanity.com/paper/2506.10532/) (2025)
- [Geometry Informed Tokenization of Molecules for Language Model Generation](https://mlsanity.com/paper/2408.10120/) (2024)
- [Unified Guidance for Geometry-Conditioned Molecular Generation](https://mlsanity.com/paper/2501.02526/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matching](https://mlsanity.com/paper/2502.15805/) (2025)
- [Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design](https://mlsanity.com/paper/2311.00462/) (2023)
- [A Review on Fragment-based De Novo 2D Molecule Generation](https://mlsanity.com/paper/2405.05293/) (2024)
- [Diffusion Twigs with Loop Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2410.24012/) (2024)
- [SynHAT: A Two-stage Coarse-to-Fine Diffusion Framework for Synthesizing Human Activity Traces](https://mlsanity.com/paper/2604.14705/) (2026)
- [Structure Preserving Diffusion Models](https://mlsanity.com/paper/2402.19369/) (2024)
- [Equivariant Blurring Diffusion for Hierarchical Molecular Conformer Generation](https://mlsanity.com/paper/2410.20255/) (2024)
- [Unraveling the Potential of Diffusion Models in Small Molecule Generation](https://mlsanity.com/paper/2507.08005/) (2025)
- [3D Molecule Generation from Rigid Motifs via SE(3) Flows](https://mlsanity.com/paper/2601.16955/) (2026)
- [Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fields](https://mlsanity.com/paper/2601.21985/) (2026)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Constraint Decoupled Latent Diffusion for Protein Backmapping](https://mlsanity.com/paper/2410.13264/) (2024)
- [Predictive Feature Caching for Training-free Acceleration of Molecular Geometry Generation](https://mlsanity.com/paper/2510.04646/) (2025)
- [Molecule Generation for Target Protein Binding with Hierarchical Consistency Diffusion Model](https://mlsanity.com/paper/2503.00975/) (2025)
- [Concept-Driven Deep Learning for Enhanced Protein-Specific Molecular Generation](https://mlsanity.com/paper/2503.08160/) (2025)
- [Personalized Federated Training of Diffusion Models with Privacy Guarantees](https://mlsanity.com/paper/2504.00952/) (2025)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [Latent Diffusion-Based 3D Molecular Recovery from Vibrational Spectra](https://mlsanity.com/paper/2603.06113/) (2026)
- [Coarse-to-Fine Multi-Resolution Diffusion Models for Trajectory Generation in Urban Systems](https://mlsanity.com/paper/2608.14570/) (2026)

## Abstract (arXiv)

Generating desirable molecular structures in 3D is a fundamental problem for drug discovery. Despite the considerable progress we have achieved, existing methods usually generate molecules in atom resolution and ignore intrinsic local structures such as rings, which leads to poor quality in generated structures, especially when generating large molecules. Fragment-based molecule generation is a promising strategy, however, it is nontrivial to be adapted for 3D non-autoregressive generations because of the combinational optimization problems. In this paper, we utilize a coarse-to-fine strategy to tackle this problem, in which a Hierarchical Diffusion-based model (i.e.~HierDiff) is proposed to preserve the validity of local segments without relying on autoregressive modeling. Specifically, HierDiff first generates coarse-grained molecule geometries via an equivariant diffusion process, where each coarse-grained node reflects a fragment in a molecule. Then the coarse-grained nodes are decoded into fine-grained fragments by a message-passing process and a newly designed iterative refined sampling module. Lastly, the fine-grained fragments are then assembled to derive a complete atomic molecular structure. Extensive experiments demonstrate that HierDiff consistently improves the quality of molecule generation over existing methods