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Concept Reachability in Diffusion Models: Beyond Dataset Constraints
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Synthetic and Stable Diffusion experiments show that concept reachability via steering (prompt-space or h-space vectors) outlasts prompting under scarce, underspecified, or biased training data, with a sharp reachability threshold near 1% concept presence.
Problem
When can a concept be reliably reached in text-to-image diffusion models, via prompting or via activation steering, given dataset limitations such as scarcity, caption underspecification, and concept biases?
Approach
Designs a controllable synthetic dataset of two coloured shapes with systematically varied concept scarcity, caption specification, and tied concepts, and measures reachability of prompting versus two steering methods (prompt-embedding offset and U-net bottleneck h-space offset) optimised on a small set of target images.
Key results
- Steering on prompt space matches prompting under balanced data (accuracy above 0.9), while h-space accuracy drops as more concepts are modified.
- Reachability drops sharply when a concept's presence falls below roughly 1% of the training set (phase-transition-like threshold), with steering declining less than prompting.
- For positionally OOD combinations with zero training presence, prompting fails while prompt-space steering achieves over 50% accuracy when reducing the square concept.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use prompt-space steering instead of direct prompting | Synthetic diffusion models trained on balanced data · Balanced synthetic dataset | accuracy | Helped |
| Use h-space steering instead of prompt-space steering | Synthetic diffusion models trained on balanced data · Balanced synthetic dataset; targets with more modified concepts | accuracy | Hurt |
| Use prompt-space steering instead of prompting | Synthetic diffusion models with scarce concepts · Concept presence below the reachability threshold | accuracy: 0.01 | Helped |
| Reduce concept presence below the critical threshold | Synthetic diffusion models · Scarcity of concepts | accuracy: 0.01 | Hurt |
| Use prompt-space steering to reach a positionally unseen square concept | Synthetic diffusion models · Square in the front absent from training | accuracy: more than 50% | Helped |
| Remove concept information from training captions | Synthetic diffusion models · Caption underspecification | accuracy: below $0.30$ | Hurt |
| Use prompt-space or h-space steering instead of prompting | Synthetic diffusion models trained with reduced caption specification · Caption underspecification | accuracy | Helped |
| Use prompt-space steering rather than h-space steering | Synthetic diffusion models trained with reduced caption specification · Caption underspecification | accuracy | Helped |
| Use steering instead of prompting to disentangle tied concepts | Synthetic diffusion models with biased concept co-occurrences · Compositionally OOD concept combinations | accuracy | Helped |
| Increase the presence of non-circular blue shapes | Synthetic diffusion models trained with blue-circle bias · Separate reachability of tied concepts | accuracy | Helped |
| Remove only the target concept combination from training | Synthetic diffusion models · Simple compositional OOD combinations | accuracy | No clear effect |
| Use a full-target starting prompt for h-space steering | Synthetic diffusion models · Balanced data and scarcity experiments | accuracy | Helped |
Surprising findings
- Steering on the prompt space achieves over 50% accuracy on a positionally OOD target even when no training image contains the reduced concept in that position.
- Steering can reach concepts under heavy underspecification better than prompting, yet reachability still falls below 0.30 when fewer than two factors are specified.
Limitations
- Steering requires an auxiliary collection of images containing the target concept, which may be hard to obtain in real data.
- Main experiments use a small synthetic setup (3.7M-parameter U-net, two shapes per image), limiting generality to real models.
- Real-data analysis on Stable Diffusion is largely qualitative (seven examples, 50 images per concept).
Experimental setup
Datasets: Synthetic coloured-shapes dataset (54,000 images) CelebA subset (16,000 images) LAION2B-en (concept frequency statistics) ImageNet (steering images)
Benchmarks: Synthetic coloured-shapes reachability CelebA gender/hat reachability Stable Diffusion v1.5 qualitative steering
Metrics: reachability (accuracy of target concept combination)
Baselines: prompting h-space steering prompt-space steering
Builds on: Diffusion models (DDPM) Steering of h-space (Kwon et al.) Stable Diffusion
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