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Elastic property inversion remains a challenging task in quantitative interpretation and heavily relies on manual supervision. Inspired by the recent advances in deep learning techniques, particularly convolutional neural networks (CNNs) for interdisciplinary data integration, we propose a deep learning-powered workflow that enables stochastic 3D elastic property inversion by directly integrating partial-stack seismic with well logs via two multi-task CNNs, with one for initial estimation and the other for refinement. The stochasticity is introduced by contaminating local seismic patterns with Gaussian noises prior to mapping them with elastic models sampled from available elastic logs. Such a trained CNN allows running multiple realizations to estimate both baseline and uncertainty of target elastic properties. As tested over the Australian Great Exmouth dataset, the proposed workflow successfully builds a stable mapping function between near-/mid-/far/ultrafar-stack seismic and three wells and simultaneously produces volumes of density as well as P- and S-velocity. Not only both properties are observed in good match with seismic patterns and of high lateral continuity, but moreover the derived synthetic seismic is consistent with the observed full-stack seismic.