Abstract
<title>Abstract</title> <p>Population-level anatomical atlases, the canonical references that capture a population's shared geometric structure, are a cornerstone of medical image analysis. Building atlases conventionally requires explicit image registration and deformation modeling, with careful choices of registration objective and regularization tailored to each anatomical region and imaging modality. We show that diffusion models trained on one anatomical population implicitly encode a population-level canonical reference for that population, and that this reference is obtained directly by inference, without registration, fine-tuning, or atlas-specific objective. The recovered reference is the image that the model's deterministic reverse process converges to from independent noise initializations. When that convergence holds, the result is a sharp, registerable, and semantically meaningful population template. On T1-weighted brain MRIs, and despite requiring no atlas-construction step, the recovered reference is a registration target competitive with five established atlases across three labeled cohorts. The model is never trained to produce a template. It emerges from dynamics the model learned only for image synthesis. A single age-conditioned model recovers an entire family of brain atlases on demand, one for each age, reproducing the known cerebrospinal-fluid expansion of healthy aging and improves the registration target when matched to subject age. Our method also yields visually coherent canonical references on several anatomy domains (e.g. T1 and T2 brain MR, leg CT, knee MR). Our findings reposition diffusion models as not only generators, but as learned representations of population structure, and reframe atlas construction as a byproduct of generative inference.</p>