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Geometric Generative Modeling with Noise-Conditioned Graph Networks

ICML 2025 · Graph learning › GNN architectures · approach: Structural GNN variants · 0 citations (OpenAlex)

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Proposes noise-conditioned graph networks (NCGNs) and a concrete instance, Dynamic Message Passing (DMP), whose connectivity range and coarse-grained resolution change with noise level in flow-based generative models of geometric graphs.

Problem

Flow-based generative models for geometric graphs (point clouds, spatial transcriptomics, images) use graph neural networks whose architecture is fixed across noise levels, limiting expressiveness.

Approach

Make the GNN architecture a function of noise level: at high noise use coarser graphs with broader connectivity (supernodes and larger kNN range), at low noise use fine, sparse graphs; theoretically motivated by an information-theoretic analysis showing optimal aggregation radius grows with noise.

Key results

• On ModelNet40, DMP reduces Wasserstein distance vs. KNN and long-short range baselines, averaging a 16.15% improvement across GCN and GAT.
• On ImageNet 256x256 unconditional generation, DiT-DMP improves FID from 84.051 (DiT) to 63.983 at identical computational complexity.
• On spatiotemporal transcriptomics, DMP has lowest W2 on GCN in most tasks (e.g., unconditional generation 0.812 vs. 0.880 fully connected) and comparable performance on GAT.

Measured effects reported in the paper

Surprising findings

• Logarithmic adaptive schedule underperforms the baselines on ModelNet40, while the other schedules beat them.
• On spatiotemporal gene imputation and knockout, DMP shows no significant advantage over baselines, and on GAT it is comparable rather than better.

Limitations

• DMP uses a predefined range and resolution schedule rather than a learned one.
• Theoretical analysis relies on simplifying assumptions (e.g., 1D continuous graph and specific correlation form), though empirical checks are provided.
• Gains on spatiotemporal gene imputation/knockout are not significant.

Experimental setup

Datasets: ModelNet40 simulated spatiotemporal transcriptomics (reaction-diffusion) ImageNet 256x256

Benchmarks: ModelNet40 simulated spatiotemporal transcriptomics ImageNet 256x256

Metrics: Wasserstein distance (W2) FID sFID IS Precision Recall

Baselines: KNN graph GNN Long-Short Range GNN Fully connected GNN DiT Random graph

Builds on: Torsional Diffusion FlexiViT Diffusion Transformer (DiT) flow matching neighborhood attention

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