# Graph Diffusion Transformers for Multi-Conditional Molecular Generation

arXiv: https://arxiv.org/abs/2401.13858 · HTML: https://mlsanity.com/paper/2401.13858/

## Key facts

- Cited by 45 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 33 of its 50 references that are in the map.
- First posted on arXiv 24 Jan 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 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [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)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization](https://mlsanity.com/paper/2206.12411/) (2022)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [Genetic algorithms are strong baselines for molecule generation](https://mlsanity.com/paper/2310.09267/) (2023)

## Built on by (most cited first, 30 of 45)

- [Position: Graph Learning Will Lose Relevance Due To Poor Benchmarks](https://mlsanity.com/paper/2502.14546/) (2025)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [A Survey of Graph Transformers: Architectures, Theories and Applications](https://mlsanity.com/paper/2502.16533/) (2025)
- [Learning Molecular Representation in a Cell](https://mlsanity.com/paper/2406.12056/) (2024)
- [MolTextNet: A Two-Million Molecule-Text Dataset for Multimodal Molecular Learning](https://mlsanity.com/paper/2506.00009/) (2025)
- [FreeScene: Mixed Graph Diffusion for 3D Scene Synthesis from Free Prompts](https://mlsanity.com/paper/2506.02781/) (2025)
- [Learning Flexible Forward Trajectories for Masked Molecular Diffusion](https://mlsanity.com/paper/2505.16790/) (2025)
- [Graph Diffusion Transformers are In-Context Molecular Designers](https://mlsanity.com/paper/2510.08744/) (2025)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [Graph-structured Small Molecule Drug Discovery Through Deep Learning: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2502.08975/) (2025)
- [PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesis](https://mlsanity.com/paper/2509.12212/) (2025)
- [Molecular Representations in Implicit Functional Space via Hyper-Networks](https://mlsanity.com/paper/2601.22327/) (2026)
- [GoAgent: Group-of-Agents Communication Topology Generation for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2603.19677/) (2026)
- [RADAR: Redundancy-Aware Diffusion for Multi-Agent Communication Structure Generation](https://mlsanity.com/paper/2605.09907/) (2026)
- [Any-Property-Conditional Molecule Generation with Self-Criticism using Spanning Trees](https://mlsanity.com/paper/2407.09357/) (2024)
- [Instruction-Based Molecular Graph Generation with Unified Text-Graph Diffusion Model](https://mlsanity.com/paper/2408.09896/) (2024)
- [Backdoor Attacks on Discrete Graph Diffusion Models](https://mlsanity.com/paper/2503.06340/) (2025)
- [PolyGraph Discrepancy: a classifier-based metric for graph generation](https://mlsanity.com/paper/2510.06122/) (2025)
- [NNiT: Width-Agnostic Neural Network Generation with Structurally Aligned Weight Spaces](https://mlsanity.com/paper/2603.00180/) (2026)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2509.09451/) (2025)
- [FlowMS: Flow Matching for De Novo Structure Elucidation from Mass Spectra](https://mlsanity.com/paper/2603.18397/) (2026)
- [A General-Purpose Framework for Chemical Reaction Representation with Atomic Correspondence and Flexible Condition Adaptation](https://mlsanity.com/paper/2411.17629/) (2024)
- [DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform](https://mlsanity.com/paper/2504.06312/) (2025)
- [NMIRacle: Multi-modal Generative Molecular Elucidation from IR and NMR Spectra](https://mlsanity.com/paper/2512.19733/) (2025)
- [VQ-SAD: Vector Quantized Structure Aware Diffusion For Molecule Generation](https://mlsanity.com/paper/2605.00354/) (2026)
- [Controllable Molecular Generative Foundation Models](https://mlsanity.com/paper/2605.15354/) (2026)
- [From Uniform to Learned Graph Priors: Diffusion for Structure Discovery](https://mlsanity.com/paper/2606.11831/) (2026)
- [Learning Repetition-Invariant Representations for Polymer Informatics](https://mlsanity.com/paper/2505.10726/) (2025)
- [Cognitive Structure Generation: From Educational Priors to Policy Optimization](https://mlsanity.com/paper/2508.12647/) (2025)

## Abstract (arXiv)

Inverse molecular design with diffusion models holds great potential for advancements in material and drug discovery. Despite success in unconditional molecular generation, integrating multiple properties such as synthetic score and gas permeability as condition constraints into diffusion models remains unexplored. We present the Graph Diffusion Transformer (Graph DiT) for multi-conditional molecular generation. Graph DiT integrates an encoder to learn numerical and categorical property representations with the Transformer-based denoiser. Unlike previous graph diffusion models that add noise separately on the atoms and bonds in the forward diffusion process, Graph DiT is trained with a novel graph-dependent noise model for accurate estimation of graph-related noise in molecules. We extensively validate Graph DiT for multi-conditional polymer and small molecule generation. Results demonstrate the superiority of Graph DiT across nine metrics from distribution learning to condition control for molecular properties. A polymer inverse design task for gas separation with feedback from domain experts further demonstrates its practical utility.