Signal-Preserving Cosmic Microwave Background Cleaning with Multi-Scale Learning

Large-scale Cosmic Microwave Background (CMB) B-mode polarization is a key probe of inflation, but is obscured by complex Galactic dust foregrounds. Reliable foreground removal must suppress this contamination without distorting the underlying primordial signal. This is typically done with Internal Linear Combination (ILC), which requires multi-frequency data and is limited to second-order statistics. We present \textit{single}-frequency cleaning with CNNs that exploit inter-scale correlations in Galactic dust structure to estimate large-scale foregrounds from small-scale modes, while preserving the primordial signal by construction. Using only small-scale B-modes, our model reduces the MSE from $1.4\times10^{-3}\,\mu\mathrm{K}^2$ for single-channel ILC to $3.4\times10^{-4}\,\mu\mathrm{K}^2$; adding same-frequency temperature and E-polarization further reduces it to $2.1\times10^{-4}\,\mu\mathrm{K}^2$. Hybrid models combining multi-frequency information with inter-scale learning improve over ILC residuals by $\mathcal{O}(10^3)$. Our results show that inter-scale and cross-component structure offers substantial foreground cleaning information beyond multi-frequency correlations, enabling ML models that are both physically reliable and complementary to frequency-based CMB foreground removal.