# Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models

arXiv: https://arxiv.org/abs/2505.22935 · HTML: https://mlsanity.com/paper/2505.22935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 47 references that are in the map.
- First posted on arXiv 28 May 2025.

## 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 30)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [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)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Non Gaussian Denoising Diffusion Models](https://mlsanity.com/paper/2106.07582/) (2021)
- [Is Noise Conditioning Necessary for Denoising Generative Models?](https://mlsanity.com/paper/2502.13129/) (2025)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes](https://mlsanity.com/paper/2203.03060/) (2022)
- [Optimal Inference in Contextual Stochastic Block Models](https://mlsanity.com/paper/2306.07948/) (2023)
- [Hyperbolic Graph Diffusion Model](https://mlsanity.com/paper/2306.07618/) (2023)
- [Provably Robust Explainable Graph Neural Networks against Graph Perturbation Attacks](https://mlsanity.com/paper/2502.04224/) (2025)
- [GraphGUIDE: interpretable and controllable conditional graph generation with discrete Bernoulli diffusion](https://mlsanity.com/paper/2302.03790/) (2023)
- [Listening to the Noise: Blind Denoising with Gibbs Diffusion](https://mlsanity.com/paper/2402.19455/) (2024)
- [Efficient Graph Matching for Correlated Stochastic Block Models](https://mlsanity.com/paper/2412.02661/) (2024)
- [Complex contagion process in spreading of online innovation](https://mlsanity.com/paper/1405.6879/) (2014)

## Abstract (arXiv)

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4-6%) and computation time (8-10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.