Locating the persons moving through an environment without the necessity of them being equipped with special devices has become vital for many applications including security, IoT, healthcare, etc. Existing device-free indoor localization systems commonly rely on the utilization of Received Signal Strength Indicator (RSSI) and WiFi Channel State Information (CSI) techniques. However, the accuracy of RSSI is adversely affected by environmental factors like multi-path interference and fading. Additionally, the lack of standardization in CSI necessitates the use of specialized hardware and software. In this paper, we present TimeSense, a deep learning-based multi-person device-free indoor localization system that addresses these challenges. TimeSense leverages Time of Flight information acquired by the fine-time measurement protocol of IEEE 802.11-2016 standard. Specifically, the measured round trip time between the transmitter and receiver is influenced by the dynamic changes in the environment induced by human presence. TimeSense effectively detects this anomalous behavior using a stacked denoising auto-encoder model, thereby estimating the user's location. The system incorporates a probabilistic approach on top of the deep learning model to ensure seamless tracking of the users. The evaluation of TimeSene in two realistic environments demonstrates its efficacy, achieving a median localization accuracy of 1.57 and 2.65 meters. This surpasses the performance of state-of-the-art techniques by 49% and 103% in the two testbeds.