The problem of detecting and identifying sensor faults is critical for efficient, safe, regulatory-compliant, and sustainable operations of modern industrial processing systems. The increasing complexity of such systems brings, however, new challenges for sensor fault detection and sensor fault isolation (SFD-SFI). One of the key enablers for any SFD-SFI method is analytical redundancy, which is provided by an analytical model of sensor observations derived from first principles or identified from historical data. As defective sensors generate measurements that are inconsistent with their expected behavior as defined by the model, SFD amounts to the generation and monitoring of residuals between sensor observations and model predictions. In this article, we introduce a disentangled recurrent neural network (RNN) with the objective to cope with the smearing-out effect, i.e., where the propagation of a sensor fault to nonfaulty sensor results in large and misleading residuals. The introduction of a probabilistic model for the residual generation allows us to develop a novel procedure for the identification of the faulty sensors. The computational complexity of the proposed algorithm is linear in the number of sensors as opposed to the combinatorial nature of the SFI problem. Finally, we empirically verify the performance of the proposed SFD-SFI architecture using a real data set collected at a petrochemical plant.