The Variable Subset Forecasting (VSF) problem, where the majority of variables are unavailable in the inference stage of multivariate forecasting, has been an important but under-explored task with broad impacts in many real-world applications.Missing values, absent inter-correlation, and the impracticality of retraining largely hinder the ability of multivariate forecasting models to capture inherent relationships among variables, impacting their performance However, existing approaches towards these issues either heavily rely on local temporal correlation or face limitations in fully recovering missing information from the unavailable subset, accompanied by notable computational expenses.To address these problems, we propose a novel density estimation solution to recover the information of missing variables via flows-based generative framework.In particular, a novel generative network for time series, namely Time-series Reconstruction Flows (TRF), is proposed to estimate and reconstruct the missing variable subset.In addition, a novel meta-training framework, Variable-Agnostic Meta Learning, has been developed to enhance the generalization ability of TRF, enabling it to adapt to diverse missing variables situations.Finally, extensive experiments are conducted to demonstrate the superiority of our proposed method compared with baseline methods.