# From Uniform to Learned Graph Priors: Diffusion for Structure Discovery

arXiv: https://arxiv.org/abs/2606.11831 · HTML: https://mlsanity.com/paper/2606.11831/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Graph Diffusion Transformers for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2401.13858/) (2024)
- [Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation](https://mlsanity.com/paper/2402.03687/) (2024)
- [Neural Relational Inference with Efficient Message Passing Mechanisms](https://mlsanity.com/paper/2101.09486/) (2021)
- [Predicting the Dynamics of Complex System via Multiscale Diffusion Autoencoder](https://mlsanity.com/paper/2505.02450/) (2025)
- [A Graph Dynamics Prior for Relational Inference](https://mlsanity.com/paper/2306.06041/) (2023)

## Built on by (most cited first, 1 of 1)

- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges. However, these methods typically rely on oversimplified, factorized graph priors. Such priors, typically nearing uniform distributions, treat edges as independent entities. This systemic misalignment does not match the real-world systems and yields diffuse and indecisive edge posteriors limiting the reliability of structural discovery. To address this, we propose textitDiff-prior, a diffusion-parameterized adaptive prior used to calibrate latent graph distribution rather than generate graphs. Our core insight is to reframe prior integration as a learnable denoising-style calibration that organizes scattered, uncertain edge posteriors into a more reliable overall structure which can be trained by the diffusion model. Diff-prior learns an adaptive structure prior that performs structured calibration on the edge posteriors during inference, guiding it towards a distribution closer to the underlying structure. The diff-prior operates before structural sampling and acts as a denoising calibrator directly on the encoder edge distribution, which provides a generic training paradigm over structured variables. Experiments on standard benchmarks validated our framework, and the results indicate that Diff-prior improves the performance of structure inference and generates more decisive edge posteriors across multiple NRI-family architectures. The code is available on https://github.com/Hardy158118/Diffprior.