Every Sample Speaks Volumes: Steering 3D MRI Generators Under a Measured Contract

Controlled experiments in neuroimaging often require volumes that real cohorts cannot provide, such as the same brain with and without a specified degree of Alzheimer's disease (AD) atrophy. Pretrained generators of 3D brain MRI could provide such volumes without retraining. However, inference-time guidance fixes only the direction and strength of a change. It neither specifies the magnitude of the change nor bounds its effect on other structures, and it does not verify the output. We propose a closed-loop controller that obtains from a frozen generator a volume satisfying a verifiable specification, which we call a contract. A contract requests a change in the volume of one anatomical structure and bounds the change of every other planned structure. Both are read by an external segmentation tool, the verifier, in units of its test-retest variability. The controller generates pairs of volumes from the same noise with perturbations of opposite sign. After each pair, it updates a local linear model of the verifier's response with a rank-one correction. It returns a volume only when the contract holds within a fixed budget of pairs. On five released generators from four model families, a single configuration satisfies the contract in 84 to 100% of held-out requests. In contrast, gradient-guidance methods with step sizes fixed in advance satisfy it in at most 28%. An AD classifier built on a second, independent segmentation tool scores volumes steered to the full disease profile above their unsteered counterparts. The procedure also transfers to a frozen physics emulator.