# Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models

arXiv: https://arxiv.org/abs/2404.15625 · HTML: https://mlsanity.com/paper/2404.15625/

## Key facts

- Cited by 22 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 34 of its 59 references that are in the map.
- First posted on arXiv 24 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, 30 of 34)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)
- [Line Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2010.10046/) (2020)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [Raising the Bar in Graph-level Anomaly Detection](https://mlsanity.com/paper/2205.13845/) (2022)
- [Learning Graph-Level Representation for Drug Discovery](https://mlsanity.com/paper/1709.03741/) (2017)
- [DiffGuard: Semantic Mismatch-Guided Out-of-Distribution Detection using Pre-trained Diffusion Models](https://mlsanity.com/paper/2308.07687/) (2023)
- [MolGrow: A Graph Normalizing Flow for Hierarchical Molecular Generation](https://mlsanity.com/paper/2106.05856/) (2021)
- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [Orthogonal Graph Neural Networks](https://mlsanity.com/paper/2109.11338/) (2021)

## Built on by (most cited first, 22 of 22)

- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [Unifying Unsupervised Graph-Level Anomaly Detection and Out-of-Distribution Detection: A Benchmark](https://mlsanity.com/paper/2406.15523/) (2024)
- [Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformation](https://mlsanity.com/paper/2405.14407/) (2024)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Adaptive Multi-prompt Contrastive Network for Few-shot Out-of-distribution Detection](https://mlsanity.com/paper/2506.17633/) (2025)
- [Rethinking Independent Cross-Entropy Loss For Graph-Structured Data](https://mlsanity.com/paper/2405.15564/) (2024)
- [Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space](https://mlsanity.com/paper/2501.15461/) (2025)
- [Graph Defense Diffusion Model](https://mlsanity.com/paper/2501.11568/) (2025)
- [BOOM: Benchmarking Out-Of-distribution Molecular Property Predictions of Machine Learning Models](https://mlsanity.com/paper/2505.01912/) (2025)
- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps](https://mlsanity.com/paper/2505.15177/) (2025)
- [Learnable Kernel Density Estimation for Graphs and Its Application to Graph-Level Anomaly Detection](https://mlsanity.com/paper/2505.21285/) (2025)
- [Can Molecular Foundation Models Know What They Don't Know? A Simple Remedy with Preference Optimization](https://mlsanity.com/paper/2509.25509/) (2025)
- [Coarse-to-Fine Open-Set Graph Node Classification with Large Language Models](https://mlsanity.com/paper/2512.16244/) (2025)
- [From Subtle to Significant: Prompt-Driven Self-Improving Optimization in Test-Time Graph OOD Detection](https://mlsanity.com/paper/2602.17342/) (2026)
- [What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition](https://mlsanity.com/paper/2605.13032/) (2026)
- [Soft causal learning for generalized molecule property prediction: An environment perspective](https://mlsanity.com/paper/2505.06283/) (2025)
- [Prompt Optimization Meets Subspace Representation Learning for Few-shot Out-of-Distribution Detection](https://mlsanity.com/paper/2509.18111/) (2025)
- [Out-of-Distribution Detection in Molecular Complexes via Diffusion Models for Irregular Graphs](https://mlsanity.com/paper/2512.18454/) (2025)
- [Learning to Explore: Policy-Guided Outlier Synthesis for Graph Out-of-Distribution Detection](https://mlsanity.com/paper/2603.00602/) (2026)
- [Autonomous Drift Learning in Data Streams: A Unified Perspective](https://mlsanity.com/paper/2605.01295/) (2026)
- [Node-level Graph Neural Architecture Search Framework](https://mlsanity.com/paper/2610.09297/) (2026)

## Abstract (arXiv)

The open-world test dataset is often mixed with out-of-distribution (OOD) samples, where the deployed models will struggle to make accurate predictions. Traditional detection methods need to trade off OOD detection and in-distribution (ID) classification performance since they share the same representation learning model. In this work, we propose to detect OOD molecules by adopting an auxiliary diffusion model-based framework, which compares similarities between input molecules and reconstructed graphs. Due to the generative bias towards reconstructing ID training samples, the similarity scores of OOD molecules will be much lower to facilitate detection. Although it is conceptually simple, extending this vanilla framework to practical detection applications is still limited by two significant challenges. First, the popular similarity metrics based on Euclidian distance fail to consider the complex graph structure. Second, the generative model involving iterative denoising steps is time-consuming especially when it runs on the enormous pool of drugs. To address these challenges, our research pioneers an approach of Prototypical Graph Reconstruction for Molecular OOD Detection, dubbed as PGR-MOOD and hinges on three innovations: i) An effective metric to comprehensively quantify the matching degree of input and reconstructed molecules; ii) A creative graph generator to construct prototypical graphs that are in line with ID but away from OOD; iii) An efficient and scalable OOD detector to compare the similarity between test samples and pre-constructed prototypical graphs and omit the generative process on every new molecule. Extensive experiments on ten benchmark datasets and six baselines are conducted to demonstrate our superiority.