# Diffusion model for relational inference

**Authors:** Shuhan Zheng, Ziqiang Li, Kantaro Fujiwara, Gouhei Tanaka  
**arXiv:** [2401.16755](https://arxiv.org/abs/2401.16755)  
**Date:** 2024-01-30  
**Summary page:** https://www.summarizepaper.com/en/paper/2401.16755v1/

## Key points

- Researchers address the challenge of uncovering interaction relations in complex systems using observable dynamics
- Proposed approach called Diffusion model for Relational Inference (DiffRI) aims to learn probability of connections between components through conditional diffusion modeling
- DiffRI outperforms other state-of-the-art models in discovering ground truth interactions in an unsupervised manner
- Experiments demonstrate competence of DiffRI in inferring latent edges within underlying graphs representing system components
- DiffRI model combines diffusion model for time series imputation with an interaction estimation process to enhance relational inference from time series data

## Summary

In their study "Diffusion model for relational inference," researchers Shuhan Zheng, Ziqiang Li, Kantaro Fujiwara, and Gouhei Tanaka address the challenge of uncovering interaction relations in complex interacting systems using observable dynamics. This problem, known as relational inference, is a crucial aspect of understanding dynamical behaviors in various systems. To tackle this issue, the researchers propose a novel approach called Diffusion model for Relational Inference (DiffRI), inspired by a self-supervised method for probabilistic time series imputation. The DiffRI model aims to learn the probability of connections between components in a system through conditional diffusion modeling. By leveraging this approach, the researchers demonstrate that DiffRI outperforms other state-of-the-art models in discovering ground truth interactions in an unsupervised manner. The experiments conducted on simulated and quasi-real datasets showcase the competence of DiffRI in inferring latent edges within underlying graphs representing system components. Unlike existing prediction-based VAE frameworks commonly used in related works, the DiffRI model combines a diffusion model for time series imputation with an interaction estimation process to enhance relational inference from time series data. The mathematical formulation of the relational inference problem is presented, defining multivariate time series data X as representing the time evolution of states in a system with K components over L time steps. The static connectivity between components is represented by a fixed graph G = {V,E}, where vertices v correspond to system components and edges e represent their connectivity. The goal of this study is to infer latent edges E in the underlying graph G based on multivariate time series data provided. The methodology section introduces the DiffRI framework as a generative model designed specifically for inferring relations between interacting components from time series data. The concept and overview of DiffRI are detailed, highlighting its effectiveness in reconstructing interaction relationships within complex systems. Overall, this study contributes valuable insights into relational inference techniques for understanding dynamical behaviors in various interacting systems.