Measurement-Aligned Diffusion: Closing the Loop Between Generative Models and Catalog Measurements

Using a generative model as a scientific instrument requires more than plausible images: catalog controls must be meaningful, behaviorally faithful, and testable against real observations. We use an eight-dimensional catalog vector—redshift, multiband fluxes, ellipticity, effective radius, and S\'ersic index—as an interpretable interface to a conditional diffusion model, aligned by a frozen, non-adaptive measurement proxy. On the test set of $2,145$ real images, the proxy has mean $R^2=0.925$ and degrades in the extreme S\'ersic tail. With that proxy fixed, six one-coordinate counterfactual paths track the requested axis with Spearman correlation at least $0.96$, and leave-group ablations raise the error on the removed axes, most strongly for shape and scale. On $100$ matched catalog conditions, alignment lowers the closed-loop error of this same proxy by $56.4\%$ when sampling from noise and by $58.4\%$ in image-to-image sampling, relative to an unaligned diffusion baseline. Accepted samples then retrieve real galaxies. In leave-one-out rare-object search over $46,130$ catalog images, Recall@500 is $0.588$, compared with $0.052$ for catalog-space nearest neighbors. Screening $3,128,494$ cutouts with $461$ prototypes, two blinded experts mark $79.5\%$ of their judgments on $100$ pairs drawn from the top-50 neighbors as visually similar. Closed-loop scores measure consistency with the fixed proxy; retrieval and expert judgments test the outputs on real survey images. The same interface can then query future wide-field surveys by rendering a stated catalog hypothesis as a prototype and matching it to real cutouts.