Despite the remarkable progress of deep-learning methods generating a target vital sign waveform from a source vital sign waveform, most existing models are designed exclusively for a specific source-to-target pair. This requires distinct model architectures, optimization procedures, and pre-processing pipelines, resulting in multiple models that hinder usability in clinical settings. To address this limitation, we propose the Multi-Directional Vital-Sign Converter (MD-ViSCo), a unified framework capable of generating any target waveform such as electrocardiogram (ECG), photoplethysmogram (PPG), or arterial blood pressure (ABP) from any single input waveform with a single model. MD-ViSCo employs a shallow 1-Dimensional U-Net integrated with a Swin Transformer that leverages Adaptive Instance Normalization (AdaIN) to capture distinct waveform styles. To evaluate the efficacy of MD-ViSCo, we conduct multi-directional waveform generation on two publicly available datasets. Our framework surpasses state-of-the-art baselines (NabNet & PPG2ABP) on average across all waveform types, lowering Mean absolute error (MAE) by 8.8% and improving Pearson correlation (PC) by 4.9% over two datasets. In addition, the generated ABP waveforms satisfy the Association for the Advancement of Medical Instrumentation (AAMI) criterion and achieve Grade B on the British Hypertension Society (BHS) standard, outperforming all baselines. By eliminating the need for developing a distinct model for each task, we believe that this work offers a unified framework that can deal with any kind of vital sign waveforms with a single model in healthcare monitoring.