Concept Reachability in Diffusion Models: Beyond Dataset Constraints

TL;DR

We address the problem of concept reachability in diffusion models when prompts alone fail to access target concepts, due to dataset constraints such as scarcity, underspecification, and biases. The authors introduce a synthetic dataset and a two-space steering framework (prompt-space and $h$-space) to study reachability, supplemented by real-data validation on Stable Diffusion and CelebA. Key findings include a phase-transition-like behavior where reachability rapidly increases once a very small concept prevalence threshold is crossed (approximately $p_\mathcal{X}(f) \approx 0.01$), and that steering can reliably access concepts when prompting cannot, with prompt-space steering often outperforming $h$-space steering under underspecification. The work provides practical guidance for model providers to enable user-facing latent-space control as an alternative to costly data curation or retraining, with demonstrated relevance to real-world diffusion systems.

Abstract

Despite significant advances in quality and complexity of the generations in text-to-image models, prompting does not always lead to the desired outputs. Controlling model behaviour by directly steering intermediate model activations has emerged as a viable alternative allowing to reach concepts in latent space that may otherwise remain inaccessible by prompt. In this work, we introduce a set of experiments to deepen our understanding of concept reachability. We design a training data setup with three key obstacles: scarcity of concepts, underspecification of concepts in the captions, and data biases with tied concepts. Our results show: (i) concept reachability in latent space exhibits a distinct phase transition, with only a small number of samples being sufficient to enable reachability, (ii) where in the latent space the intervention is performed critically impacts reachability, showing that certain concepts are reachable only at certain stages of transformation, and (iii) while prompting ability rapidly diminishes with a decrease in quality of the dataset, concepts often remain reliably reachable through steering. Model providers can leverage this to bypass costly retraining and dataset curation and instead innovate with user-facing control mechanisms.

Figures (22)

• Figure 1: Images generated by Stable Diffusion latent_diff that fail to produce the desired outcome due to hypothesised dataset limits: (L) a scarce concept, (C) underspecification in a caption, (R) biases. See Appendix \ref{['app:train_stable']} for details.
• Figure 2: Visualisation of the structure of the dataset according to concepts of interest (in the diagram, three). Each block in the cube represents the collections of images in $[f_1^{(i)}, f_2^{(j)}, f_3^{(k)}]_\mathcal{X}$. A darker shade represents a higher number of images in the block. Data modifications are as described in Section \ref{['sec:problems']}.
• Figure 3: Concepts of interest in the dataset. The concepts of an image are summarised as the tuple $(c_1, s_1, c_2, s_2)$, where each of these positions refers to back colour, back shape, front colour and front shape respectively. In the diagram, this is $(blue, circle, red, triangle)$.
• Figure 4: Reachability to different concept combinations when prompting, as well as steering from the starting prompt $y_s =$"a green triangle behind a red triangle". Target colour-shape combinations (note that the relative position is representative) are shown at the top of each bar, and are organised according to the number of concepts that differ from the concepts of $y_s$.
• Figure 5: Accuracy of prompting and steering on the prompt space and $h$-space to $(red, triangle, green, square)$ for starting prompt $y_s =$ "a red triangle behind a green square" and varying proportion $p_\mathcal{X}$ of images in the dataset containing the concepts $c_1 = red$ (top) and $s_2 = square$ (bottom) across the dataset. The dashed red line marks the approximate threshold 0.01 of the shift in reachability.

Theorems & Definitions (4)

• Definition 3.1: Concept Reachability
• Definition 3.2: Out-of-distribution
• Definition 3.3: Compositionally out-of-distribution
• Definition 3.4: Positionally out-of-distribution