# Diffusion Twigs with Loop Guidance for Conditional Graph Generation

arXiv: https://arxiv.org/abs/2410.24012 · HTML: https://mlsanity.com/paper/2410.24012/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 80 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 30 of 59)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [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)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Molecular De Novo Design through Deep Reinforcement Learning](https://mlsanity.com/paper/1704.07555/) (2017)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [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)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (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)

## Built on by (most cited first, 4 of 4)

- [Straight-Line Diffusion Model for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2503.02918/) (2025)
- [CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homology](https://mlsanity.com/paper/2512.19736/) (2025)
- [Fine-Grained Graph Generation through Latent Mixture Scheduling](https://mlsanity.com/paper/2605.02780/) (2026)
- [A Systematic Evaluation of Molecule Generation Models for De Novo Drug Design: From Benchmarks to Practical Insights](https://mlsanity.com/paper/2609.10099/) (2026)

## Abstract (arXiv)

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.