Gesture-driven music generation is an emerging human-computer interaction paradigm for touch-free and expressive musical interaction. However, many existing approaches treat the task as isolated gesture classification or map gestures to symbolic outputs such as MIDI followed by a separate rendering stage, which limits temporal continuity and real-time responsiveness. This work presents Gesture2Music, a low-latency streaming framework for continuous gesture-driven music generation from live webcam feed. The system processes sequences of body and hand landmarks and uses a causal temporal convolutional network (TCN) to predict note-level musical control events, including pitch, octave, onset, sustain, amplitude, and activity state. Because available gesture-note datasets typically contain only isolated single-note recordings rather than continuous performance sequences, a synthetic stream generation strategy is introduced to construct continuous gesture streams by concatenating single-note clips and deriving heuristic temporal event labels. Temporal consistency and spectral proxy losses are further used to reduce prediction jitter and encourage audio-consistent outputs. During inference, predicted musical events are rendered into continuous music using predefined note samples with rhythmic quantization and scale-constrained filtering for improved musical stability. Experiments on a custom gesture-to-music dataset with 21 gesture-note classes spanning seven tones across three pitch levels demonstrate stable real-time performance, low inference latency of 30\,ms, and improved temporal continuity.