In this paper, we introduce Neural Mapper for Vector Quantized Time Series Generator (NM-VQTSG), a novel method aimed at addressing fidelity challenges in vector quantized (VQ) time series generation. VQ-based methods, such as TimeVQVAE, have demonstrated success in generating time series but are hindered by two critical bottlenecks: information loss during compression into discrete latent spaces and deviations in the learned prior distribution from the ground truth distribution. These challenges result in synthetic time series with compromised fidelity and distributional accuracy. To overcome these limitations, NM-VQTSG leverages a U-Net-based neural mapping model to bridge the distributional gap between synthetic and ground truth time series. To be more specific, the model refines synthetic data by addressing artifacts introduced during generation, effectively aligning the distributions of synthetic and real data. Importantly, NM-VQTSG can be used for synthetic time series generated by any VQ-based generative method. We evaluate NM-VQTSG across diverse datasets from the UCR Time Series Classification archive, demonstrating its capability to consistently enhance fidelity in both unconditional and conditional generation tasks. The improvements are evidenced by significant improvements in FID, IS, and conditional FID, additionally backed up by visual inspection in a data space and a latent space. Our findings establish NM-VQTSG as a new method to improve the quality of synthetic time series. Our implementation is available on \url{https://github.com/ML4ITS/TimeVQVAE}.