Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models
This work addresses the problem of simplifying and improving efficiency in graph diffusion models for machine learning researchers, though it appears incremental as it builds on existing models like GDSS and DiGress.
The paper challenges the necessity of explicit noise-level conditioning in Graph Diffusion Models (GDMs) by showing that denoisers can implicitly infer noise levels from corrupted graph structures, achieving comparable or superior performance to conditioned models with reductions in parameters (4-6%) and computation time (8-10%).
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.