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

TL;DR

This paper demonstrates that graph diffusion models can operate effectively without explicit noise conditioning by leveraging the implicit noise inference capabilities of denoisers, leading to simpler and more efficient architectures.

Contribution

The work provides a theoretical framework and empirical evidence showing that explicit noise conditioning in GDMs may be unnecessary, challenging a common assumption in the field.

Findings

Unconditional GDMs perform comparably or better than conditioned models.

Unconditional models reduce parameters by 4-6% and computation time by 8-10%.

High-dimensional graph data encodes sufficient information for denoising.

Abstract

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.