The development of robust generative models for highly varied non-stationary time series data is a complex yet important problem. Traditional models for time series data prediction, such as Long Short-Term Memory (LSTM), are inefficient and generalize poorly as they cannot capture complex temporal relationships. In this paper, we present a probabilistic generative model that can be trained to capture temporal information, and that is robust to data errors. We call it Time Deep Latent Gaussian Model (tDLGM). Its novel architecture is inspired by Deep Latent Gaussian Model (DLGM). Our model is trained to minimize a loss function based on the negative log loss. One contributing factor to Time Deep Latent Gaussian Model (tDLGM) robustness is our regularizer, which accounts for data trends. Experiments conducted show that tDLGM is able to reconstruct and generate complex time series data, and that it is robust against to noise and faulty data.