To address the issues of information redundancy and temporal information decay in modeling nonlinear dynamic industrial processes, a dynamic soft sensing algorithm based on a dual-stream memory-regulated gated recurrent unit (GRU) with an embedded two-stage attention mechanism is proposed. On one hand, a dual-stream information extraction structure is designed to capture both time-related and dynamic causal correlations by introducing time gates and causal gates into the GRU, thus forming complementary information flows and enhancing model prediction performance. On the other hand, feature attention and temporal attention mechanisms are introduced during the feature extraction and prediction output stages, respectively, to dynamically uncover the latent correlations between input and target features, capture key features, and assess the importance of different historical time points for the prediction target, thereby selecting critical time point information. Finally, the proposed algorithm's prediction performance is validated through numerical simulations and soft sensing of SO₂ concentration in flue gas emissions from a thermal power plant desulfurization process.