When Simulator Targets Suppress Diversity in Conditional Diffusion: Evidence from ECG Generation

Matching a diffusion model's clean-signal estimate to a deterministic class template penalises within-class variation. We derive this penalty and show that the population-optimal estimate's variance contracts by $(1+\lambda {\mu }_i{)}^{-2}$ along eigenvectors of $A^{\top }A$, where $A$ is the coupling operator, $\lambda$ the coupling strength, and ${\mu }_i$ the corresponding eigenvalue. Template accuracy does not enter this factor. A reverse-chain covariance recursion, exact under Gaussian assumptions, predicts sampled variance ratios in synthetic experiments without fitted parameters. On patient-disjoint PTB-XL beats, with templates fitted without test patients, point coupling reduces pooled within-class standard deviation to $0.66$ of real data and increases raw-signal ${\mathrm{MMD}}^2$ by $3.7\times$ under a shared kernel. Improving the simulator, using an oracle class mean, or drawing an independent random target does not recover the lost diversity. Training the morphology and inter-lead terms separately shows that each suppresses diversity: the inter-lead term contracts the limb leads it references without improving their amplitude-normalised consistency. A constructed beat satisfies SE-Diff's released inter-lead penalty while violating Einthoven's law among its generated leads, and the released paired evaluation ranks the most concentrated generator best. Moment matching, spread matching, and exact lead identities reduce the distributional penalty; spread matching with exact identities reaches $1.3\times$ the unregularised model's raw-signal ${\mathrm{MMD}}^2$. No tested coupling improves within-PTB-XL downstream classification over the unregularised baseline beyond seed variability. Experiments on MIMIC-IV-ECG, multi-beat windows, and a small latent model reproduce the contraction. These results support avoiding deterministic template matching when within-class variation matters. They do not establish that simulator priors or sample-dependent constraints are ineffective in general.