From Seeds to Semantics: Measuring Semantic Accessibility in Deterministic Diffusion Models

Diffusion models generate samples through a sequence of learned denoising steps, and recent work has studied how semantic structure appears along this sampling process. We study this question in deterministic samplers by measuring semantic accessibility: how much information about a final semantic property (e.g. an image class label or attribute) can be extracted from the seed and intermediate states along the trajectory that produces the sample. Using DDIM sampling, for which each initial noise seed maps to a single trajectory and final image, we train a separate classifier (a probe) at several points along the trajectory to predict a semantic property of the final image. We measure how well such property can be predicted from the state at that point using using top-1 accuracy and normalized mutual information. Across MNIST, Fashion-MNIST, CIFAR-10, and CelebA, class labels and image attributes can be predicted above chance from the initial noise seed, and along DDIM trajectories, this accessibility exceeds matched-noise forward baselines. We observe that accessibility is substantially higher in groups of trajectories whose final images are classified with high confidence than in those classified with low confidence. These measurements provide a quantitative view of when semantic properties can be recovered along deterministic generation.