This paper introduces a novel deep-learning-based data assimilation scheme called Multi-domain Encoder-Decoder Latent Data Assimilation (MEDLA), which addresses the challenges of handling diverse data sources and complex, non-explicit state-observation mappings in high-dimensional dynamical systems. MEDLA leverages a multi-domain encoder-decoder architecture to encode both state and observation variables into a common latent space, eliminating the need for explicit mapping functions. This approach reduces computational costs and enhances assimilation accuracy by minimizing interpolation and approximation errors. Extensive numerical experiments, including the 2D Burgers' equation, multiphase flow simulations, and microfluidic drop interactions, demonstrate MEDLA's superior performance compared to state-of-the-art latent data assimilation methods. The results highlight MEDLA's ability to handle multi-scale observational data and complex, non-explicit mapping functions, making it a promising solution for real-time forecasting and data assimilation in high-dimensional dynamical systems.This paper introduces a novel deep-learning-based data assimilation scheme called Multi-domain Encoder-Decoder Latent Data Assimilation (MEDLA), which addresses the challenges of handling diverse data sources and complex, non-explicit state-observation mappings in high-dimensional dynamical systems. MEDLA leverages a multi-domain encoder-decoder architecture to encode both state and observation variables into a common latent space, eliminating the need for explicit mapping functions. This approach reduces computational costs and enhances assimilation accuracy by minimizing interpolation and approximation errors. Extensive numerical experiments, including the 2D Burgers' equation, multiphase flow simulations, and microfluidic drop interactions, demonstrate MEDLA's superior performance compared to state-of-the-art latent data assimilation methods. The results highlight MEDLA's ability to handle multi-scale observational data and complex, non-explicit mapping functions, making it a promising solution for real-time forecasting and data assimilation in high-dimensional dynamical systems.