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Can Diffusion Models Learn Hidden Inter-Feature Rules Behind Images?
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Shows that diffusion models capture coarse inter-feature rules but fail on fine-grained ones using four synthetic tasks, proves a constant DSM rule-conformity error, and finds classifier guidance only gives limited gains.
Problem
Whether diffusion models learn hidden inter-feature rules (conditional dependencies such as shadow length vs. sun height) between image features, beyond matching the joint distribution and FID.
Approach
Designs four controllable synthetic image tasks with coarse and fine-grained rules, evaluates DDPM rule conformity via color-mask feature extraction, gives a theoretical constant-error lower bound for DSM-trained two-layer score networks, and tests classifier guidance and filtering as mitigation.
Key results
- DDPM generated almost no coarse-rule violations across Tasks A-D (at most one in Task A) but fine-grained rule fit R^2 stayed around 0.57-0.85 across tasks.
- Classifier guidance and filtering reduced Error (e.g., Task A 0.25 to 0.17 with filtering) and raised R^2 (Task C 0.57 to 0.67 with guidance), a limited improvement.
- Theory: a two-layer DSM-trained score network has a constant rule-conforming error (bias plus variance) at any stationary point.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add contrastive-classifier guidance during sampling | DDPM · Task A | Error: 0.25 -> 0.21 | Helped |
| Add contrastive-classifier guidance during sampling | DDPM · Task B | Error: 0.11 -> 0.10 | Helped |
| Add contrastive-classifier guidance during sampling | DDPM · Task C | Error: 0.41 -> 0.26 | Helped |
| Add contrastive-classifier guidance during sampling | DDPM · Task D | Error: 0.46 -> 0.43 | Helped |
| Filter samples using a raw-image classifier | DDPM · Task A | Error: 0.25 -> 0.17 | Helped |
| Filter samples using a raw-image classifier | DDPM · Task B | Error: 0.11 -> 0.05 | Helped |
| Filter samples using a raw-image classifier | DDPM · Task C | Error: 0.41 -> 0.25 | Helped |
| Filter samples using a raw-image classifier | DDPM · Task D | Error: 0.46 -> 0.39 | Helped |
| Train for 400 rather than 200 epochs (ablation) | DDPM · Task A | R²: 0.19 -> 0.85 | Helped |
| Increase training from 400 to 4000 epochs (ablation) | DDPM · Task A | R²: R² remaining around 0.85 | No clear effect |
| Replace U-Net with larger DiT or SiT backbones (ablation) | DDPM · Task A | Fine-grained rule learning | No clear effect |
| Increase training data from 4000 to 20000 or 40000 samples (ablation) | DDPM · Task A | R² | No clear effect |
Surprising findings
- Increasing training epochs, model size (DiT/SiT), training data, or resolution did not improve fine-grained rule learning.
- A low-FID Gaussian mixture example shows FID=0 while inter-feature dependence is wrong.
Limitations
- Mitigation relies on prior knowledge of fine-grained rules to construct contrastive data, unavailable in real-world settings.
- Classifier accuracy on fine-grained contrast pairs only 60-80%, limiting guidance gains.
- Real-world evaluation uses small manual samples (5 generations per prompt) and synthetic tasks are simple 32x32 images.
Experimental setup
Datasets: synthetic Tasks A-D (32x32 images, generated by authors)
Benchmarks: synthetic Tasks A-D
Metrics: R^2 Error (bias + variance) invalid ratio coarse-grained violation count nearest-neighbor distance
Baselines: DDPM Guided DDPM Filtered DDPM
Builds on: DDPM classifier guidance SimCLR NT-Xent loss DiT SiT
Closest papers by meaning
- Simplified and Generalized Masked Diffusion for Discrete Data (NeurIPS 2024 · similarity 0.86)
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- CleanDIFT: Diffusion Features without Noise (CVPR 2025 · similarity 0.86)
- Tracing the Roots: Leveraging Temporal Dynamics in Diffusion Trajectories for Origin Attribution (NeurIPS 2025 · similarity 0.86)
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