This paper introduces a novel deep learning-based data assimilation scheme called Multi-domain Encoder-Decoder Latent Data Assimilation (MEDLA) for latent data assimilation in high-dimensional dynamical systems. The proposed method addresses the challenges of handling complex, nonlinear state-observation mappings and heterogeneous latent spaces by using a shared latent space and a multi-domain encoder-decoder architecture. MEDLA reduces computational burden by mimicking complex mapping functions with neural networks and enhances assimilation accuracy by minimizing interpolation and approximation errors. The method is tested on three numerical experiments: the 2D Burgers' equation, multiphase flow modeling, and microfluidic drop interactions. Results show that MEDLA outperforms existing latent data assimilation methods in terms of accuracy and efficiency, particularly in handling multi-scale observational data and non-explicit mapping functions. The approach combines the efficiency of LA+ and the generalizability of GLA/LSDA, making it a promising solution for data assimilation in high-dimensional systems.This paper introduces a novel deep learning-based data assimilation scheme called Multi-domain Encoder-Decoder Latent Data Assimilation (MEDLA) for latent data assimilation in high-dimensional dynamical systems. The proposed method addresses the challenges of handling complex, nonlinear state-observation mappings and heterogeneous latent spaces by using a shared latent space and a multi-domain encoder-decoder architecture. MEDLA reduces computational burden by mimicking complex mapping functions with neural networks and enhances assimilation accuracy by minimizing interpolation and approximation errors. The method is tested on three numerical experiments: the 2D Burgers' equation, multiphase flow modeling, and microfluidic drop interactions. Results show that MEDLA outperforms existing latent data assimilation methods in terms of accuracy and efficiency, particularly in handling multi-scale observational data and non-explicit mapping functions. The approach combines the efficiency of LA+ and the generalizability of GLA/LSDA, making it a promising solution for data assimilation in high-dimensional systems.