Numerically Converged, Physically Wrong: Reference Validity for Samplers of Diffusion Physics Emulators

Diffusion-based emulators of physical systems integrate a learned reverse process for every frame of a rollout, and cheaper samplers are judged by how closely they reproduce a fine-step reference. We ask when this yardstick can be trusted. First, we make it precise: a local error budget is the largest reverse step, at each noise level, whose endpoint stays within a tolerance of the reference. Measured with a censoring-aware protocol on pretrained autoregressive conditional diffusion models, budgets predict held-out step failures, transfer to rollout states, and follow an accuracy-limited rather than CFL-like law. Second, in a frozen evaluation on held-out physical conditions with 200-step rollouts scored against ground truth, fidelity to the reference ranks 20 coarse schedules like physical accuracy on transonic cylinder flow (Spearman $\rho =0.80$ and $0.997$ for two checkpoints) but in reverse on isotropic turbulence ($\rho =-0.88$ and $-0.92$). The inversion appears only after about 50 frames, is absent over the upstream 100-frame evaluation horizon, and has a specific cause: the deterministic reference is numerically converged yet retains less than half of the true kinetic energy. On the same time grids, stochastic updates lower the physical error from $0.70$ to $0.45$, match the model's native sampler, and restore the agreement. On an accurate incompressible-wake emulator, all samplers sit within 0.014 of the reference and the choice is moot. Budget-based schedule selection, frozen before testing, ties but does not beat direct pilot evaluation at a matched calibration budget. Before fidelity to a reference guides deployment, the reference itself must be validated on physical observables over the deployment horizon.