Generating co-speech gestures that are temporally coherent, semantically aligned with speech, and grounded with surrounding objects remains challenging. Prior speech-driven gesture models emphasize audio-gesture alignment but do not explicitly account for posture constraints or surrounding objects, failing to capture the inherent correlation between body gestures and the physical space. We present Puppeteer, a posture-aware, object-grounded co-speech gesture diffusion model operating in a causal latent space. We decompose long gestures into structured primitives and learn a causal variational