  We present a comprehensive neural architecture, the PUREPath, which leverages
a nested Probabilistic multi-modal U- Net framework, augmented by the inclusion
of probabilistic ResNet blocks in the Expanding Pathway of the decoders, to
estimate the posterior density of the Cosmic Microwave Background (CMB) signal
conditioned on the observed CMB data and the training dataset. By seamlessly
integrating Bayesian statistics and variational methods our model effectively
minimizes foreground contamination in the observed CMB maps. The model is
trained using foreground and noise contaminated CMB temperature maps simulated
at Planck LFI and HFI frequency channels 30 - 353 GHz using publicly available
Code for Anisotropies in the Microwave Background (CAMB) and Python Sky Model
(PySM) packages. During training, our model transforms initial prior
distribution on the model parameters to posterior distributions based on the
training data. From the joint full posterior of the model parameters, during
inference, a predicitve CMB posterior and summary statistics such as the
predictive mean, variance etc of the cleaned CMB map is estimated. The
predictive standard deviation map provides a direct and interpretable measure
of uncertainty per pixel in the predicted mean CMB map. The cleaned CMB map
along with the error estimates can be used for more accurate measurements of
cosmological parameters and other cosmological analyses.
