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Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation
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Proposes Simple Iterative Denoising (SID), which assumes conditional independence of intermediate noisy states to avoid compounding denoising errors, and Critical Iterative Denoising (CID), which adds a post-hoc Critic that adaptively re-noises elements for graph generation.
Problem
Discrete diffusion and discrete flow matching models for graphs suffer from compounding denoising errors because intermediate noisy states depend on each other, causing error accumulation during reverse denoising.
Approach
Assume intermediate noisy states depend only on the clean data (conditional independence), so each denoising step re-noises a predicted clean instance directly; a post-hoc Critic (trained on corruption indicators) then modulates per-element re-noising probabilities toward the data distribution.
Key results
- On ZINC250k, Mask CID reaches 99.97% validity without correction versus 98.65% for DruM and 80.40% for Marginal DDM, with Marginal SID reaching FCD 2.01 vs DruM 2.25.
- On Planar, Marginal SID achieves V.U.N. 91.3 and spectral MMD 7.62 versus 83.57 for Marginal DDM, though DruM remains best on spectral MMD (6.2).
- Mask CID reaches over 99% validity on ZINC250k with only 32 denoising steps, while Mask SID reaches 93.57% at 512 steps.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace marginal DDM sampling with marginal SID using the same denoiser (ablation) | Marginal DDM · QM9 | validity: 95.73 -> 99.67 | Helped |
| Replace marginal DDM sampling with marginal SID using the same denoiser (ablation) | Marginal DDM · ZINC250k | validity: 80.40 -> 99.50 | Helped |
| Replace mask DDM sampling with mask SID using the same denoiser (ablation) | Mask DDM · QM9 | validity: 48.38 -> 96.43 | Helped |
| Replace mask DDM sampling with mask SID using the same denoiser (ablation) | Mask DDM · ZINC250k | validity: 8.96 -> 93.85 | Helped |
| Add the Critic to Mask SID (ablation) | Mask SID · QM9 | validity: 96.43 -> 99.92 | Helped |
| Add the Critic to Mask SID (ablation) | Mask SID · ZINC250k | validity: 93.85 -> 99.97 | Helped |
| Add the Critic to Mask SID (ablation) | Mask SID · Planar | Spect.: 8.72 -> 6.40 | Helped |
| Add the Critic to Mask SID (ablation) | Mask SID · Planar | V.U.N.: 67.0 -> 66.0 | Hurt |
| Add the Critic to Mask SID (ablation) | Mask SID · SBM | Spect.: 15.05 -> 11.94 | Helped |
| Add the Critic to Mask SID (ablation) | Mask SID · SBM | V.U.N.: 17.5 -> 19.0 | Helped |
| Use Mask CID with 32 function evaluations (ablation) | Mask CID · ZINC250k | validity: 99,17 | Helped |
Surprising findings
- Mask diffusion baseline collapses on ZINC250k (8.96% validity) and Planar/SBM (0 V.U.N.), indicating severe compounding errors for mask noise.
- The Critic's gain is less pronounced on generic graphs (Planar, SBM) than on molecular graphs, and Mask CID is worse than Marginal SID on SBM V.U.N.
Limitations
- Critic doubles training and inference cost per the authors' own estimate.
- Critic gains are smaller on generic graphs (Planar, SBM) than on molecules; SBM validity remains low for mask models.
- Baseline numbers are taken from prior work with 1000 steps while the method uses 500 steps, making comparison not fully controlled; the method's noising is not a true diffusion process.
Experimental setup
Datasets: QM9 ZINC250k Planar SBM
Benchmarks: QM9 ZINC250k Planar SBM
Metrics: validity FCD NSPDK spectral MMD V.U.N. degree MMD clustering MMD orbit MMD
Baselines: GDSS DruM DiGress Marginal DDM Mask DDM
Builds on: DiGress discrete flow matching predictor-corrector sampling GPS graph transformer
Closest papers by meaning
- Generating Graphs via Spectral Diffusion (ICLR 2025 · similarity 0.91)
- Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models (NeurIPS 2025 · similarity 0.91)
- When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors (NeurIPS 2026 · similarity 0.90)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.90)
- Discrete-state Continuous-time Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.90)
- Generative Modelling of Structurally Constrained Graphs (NeurIPS 2024 · similarity 0.89)
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