arXiv:2610.34834v1 Announce Type: new Abstract: Clean-image prediction ($x$-prediction) and noise prediction yield equivalent population-optimal denoisers, yet can perform very differently in finite diffusion networks. For noisy input $Y_t$ with noise standard deviation $\sigma_t$, a noise predictor $f_{\varepsilon,t}$ induces the clean-image estimate $\widehat X_1=Y_t-\sigma_t f_{\varepsilon,t}(Y_t)$. This reveals a noise-transmission burden: the predictor must preserve information needed to cancel the input corruption. Under Gaussian corruption of $d$-dimensional data, a linear input bottleneck of rank $rSource：https://arxiv.org/abs/2610.34834
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