# Cometh: A continuous-time discrete-state graph diffusion model

arXiv: https://arxiv.org/abs/2406.06449 · HTML: https://mlsanity.com/paper/2406.06449/

## Key facts

- Cited by 32 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 48 of its 59 references that are in the map.
- First posted on arXiv 10 Jun 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 48)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [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)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Graph Inductive Biases in Transformers without Message Passing](https://mlsanity.com/paper/2305.17589/) (2023)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)

## Built on by (most cited first, 30 of 32)

- [Position: Graph Learning Will Lose Relevance Due To Poor Benchmarks](https://mlsanity.com/paper/2502.14546/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Graph Generative Pre-trained Transformer](https://mlsanity.com/paper/2501.01073/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (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)
- [Graph-GRPO: Training Graph Flow Models with Reinforcement Learning](https://mlsanity.com/paper/2603.10395/) (2026)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Generating Directed Graphs with Dual Attention and Asymmetric Encoding](https://mlsanity.com/paper/2506.16404/) (2025)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2509.09451/) (2025)
- [LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening](https://mlsanity.com/paper/2512.01190/) (2025)
- [Variational Learning for Insertion-based Generation](https://mlsanity.com/paper/2606.02133/) (2026)
- [Variational Bayesian Flow Network for Graph Generation](https://mlsanity.com/paper/2601.22524/) (2026)
- [Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation](https://mlsanity.com/paper/2603.23398/) (2026)
- [DiPhon: Diffusion on Graphons for Scalable Graph Generation](https://mlsanity.com/paper/2607.07232/) (2026)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [FAROS: Fair Graph Generation via Attribute Switching Mechanisms](https://mlsanity.com/paper/2507.03728/) (2025)
- [Discrete Bayesian Sample Inference for Graph Generation](https://mlsanity.com/paper/2511.03015/) (2025)
- [GraDE: A Graph Diffusion Estimator for Frequent Subgraph Discovery in Neural Architectures](https://mlsanity.com/paper/2602.03257/) (2026)
- [MolHIT: Advancing Molecular-Graph Generation with Hierarchical Discrete Diffusion Models](https://mlsanity.com/paper/2602.17602/) (2026)
- [Balancing Symmetry and Efficiency in Graph Flow Matching](https://mlsanity.com/paper/2602.18084/) (2026)
- [Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation](https://mlsanity.com/paper/2604.08189/) (2026)
- [Interpolating Discrete Diffusion Models with Controllable Resampling](https://mlsanity.com/paper/2604.17310/) (2026)
- [Scaling Novel Graph Generation via Lightweight Structure-Guided Autoregressive Models](https://mlsanity.com/paper/2606.04287/) (2026)
- [DBMol: Design of High-Affinity, Target-Specific Small Molecules through Structure Prediction Models](https://mlsanity.com/paper/2607.19237/) (2026)
- [TimeRoute: Time-Aware Modality Routing and Diffusion for Multi-Modal Recommendation](https://mlsanity.com/paper/2608.10983/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Stable Transformers for Graph Generation](https://mlsanity.com/paper/2609.39739/) (2026)
- [Higher-Order Molecular Grammars for Generative and Foundation Models in Chemistry](https://mlsanity.com/paper/2610.02186/) (2026)

## Abstract (arXiv)

Discrete-state denoising diffusion models led to state-of-the-art performance in graph generation, especially in the molecular domain. Recently, they have been transposed to continuous time, allowing more flexibility in the reverse process and a better trade-off between sampling efficiency and quality. Here, to leverage the benefits of both approaches, we propose Cometh, a continuous-time discrete-state graph diffusion model, tailored to the specificities of graph data. In addition, we also successfully replaced the set of structural encodings previously used in the discrete graph diffusion model with a single random-walk-based encoding, providing a simple and principled way to boost the model's expressive power. Empirically, we show that integrating continuous time leads to significant improvements across various metrics over state-of-the-art discrete-state diffusion models on a large set of molecular and non-molecular benchmark datasets. In terms of VUN samples, Cometh obtains a near-perfect performance of 99.5% on the planar graph dataset and outperforms DiGress by 12.6% on the large GuacaMol dataset.