Non-intrusive monitoring of vital signs has become increasingly important in a variety of healthcare settings. In this paper, we present PulseFi, a novel low-cost non-intrusive system that uses Wi-Fi sensing and artificial intelligence to accurately and continuously monitor heart rate and breathing rate, as well as detect apnea events. PulseFi operates using low-cost commodity devices, making it more accessible and cost-effective. It uses a signal processing pipeline to process Wi-Fi telemetry data, specifically Channel State Information (CSI), that is fed into a custom low-compute Long Short-Term Memory (LSTM) neural network model. We evaluate PulseFi using two datasets: one that we collected locally using ESP32 devices and another that contains recordings of 118 participants collected using the Raspberry Pi 4B, making the latter the most comprehensive data set of its kind. Our results show that PulseFi can effectively estimate heart rate and breathing rate in a seemless non-intrusive way with comparable or better accuracy than multiple antenna systems that can be expensive and less accessible.