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Seismic Full Waveform Inversion (FWI) is a powerful tool for subsurface estimation, but its results are inherently non-unique. By quantifying the uncertainty in FWI results, this non-uniqueness can be better characterized, leading to more reliable and insightful interpretations of the subsurface. Bayesian inference, applied through the Metropolis-Hastings MCMC algorithm, addresses this need but is computationally intensive, especially for complex forward simulations. This study proposes a deep learning-assisted workflow to improve MCMC efficiency, replacing the traditional physics-based solver (SPECFEM2D) with a Convolutional Neural Network (CNN) for data misfit calculations. Results show the CNN approach offers a 4-fold speed increase while maintaining accuracy in posterior distribution estimation, underscoring its potential as a fast, reliable alternative for complex seismic inversion tasks.