Anomalous sound detection (ASD) that relies on annotated information during training has achieved excellent performances in benchmarks such as DCASE2020 Task 2. However, annotated data may not always be available in many scenarios. The Non-linear Independent Components Estimation (NICE) has been a promising technique for anomaly detection, as it does not rely on annotated information and is capable of exact likelihood estimation. In this paper, based on the classic NICE, a dual-path NICE model (dpNICE) is proposed, which allows for two input features feeding to two pathways and provides interactive channels for interaction and fusion between the two pathways. Then, a multiple feature fusion and dpNICE-based approach is developed, which leverages information of multiple audio features and learns to detect anomalies without annotated data. Experimental results show that the AUC and pAUC performances of our method are better than other competing annotation-free methods.