Modern applications increasingly require learning and forecasting latent dynamics from high-dimensional time-series. Compared to univariate time-series forecasting, this adds a new challenge of reasoning about the latent dynamics of an unobserved abstract state. Sequential latent variable models (LVMs) present an attractive solution, although existing works either struggle with long-term forecasting or have difficulty learning across diverse dynamics. In this paper, we first present a conceptual framework of sequential LVMs to unify existing works, contrast their fundamental limitations, and identify an intuitive solution to long-term forecasting for diverse dynamics via meta-learning. We then present the first framework of few-shot forecasting for high-dimensional time-series: instead of learning a single dynamic function, we leverage data of diverse dynamics and learn to adapt latent dynamic functions to few-shot support series. This is realized via Bayesian meta-learning underpinned by: 1) a latent dynamic function conditioned on knowledge derived from few-shot support series, and 2) a meta-model that learns to extract such dynamic-specific knowledge via feed-forward embedding of support set. We compared the presented framework with a comprehensive set of baseline models trained 1) globally on the large meta-training set with diverse dynamics, and 2) individually on single dynamics, both with and without fine-tuning to k-shot support series used by the meta-models. We demonstrated that the presented framework is agnostic to the latent dynamic function of choice and, at meta-test time, is able to forecast for new dynamics given variable-shot of support series.