Q-WAM: 4-Bit Quantization of World Action Models with Action-Subspace Protection

World Action Models (WAMs) jointly generate video and robot actions through iterative diffusion and perform strongly in robotic manipulation. However, their prohibitive compute and memory costs pose substantial deployment challenges. Post-training quantization (PTQ) can reduce these costs, but existing PTQ methods such as smoothing and rotation are insufficient to maintain the precision of action generation. To overcome this limitation, we propose Q-WAM, a new 4-bit weight-activation quantization for WAMs that preserves the actions the model generates. Specifically, we introduce the Action Observability Gramian (AOG), which measures how much rounding errors in each weighted combination of a layer's input channels change the final action through all denoising steps. We also develop Action-Subspace Protection (ASP), which keeps the few most action-sensitive channel combinations in a tiny 16-bit branch and quantizes the remaining weights and activations to 4 bits. Finally, we aggregate the AOG-derived action mass across the layers of each expert to identify the experts that matter most for the generated action, and apply ASP only to those experts, thereby preserving action quality with minimal overhead. We evaluate Q-WAM on three WAMs, both in simulation and in real-world deployment. On the RoboTwin 2.0 benchmark, it reaches 89.6–93.0% average success rate, within 1.1 percentage points of the 16-bit models, while reducing the memory of the quantized blocks by 3.1–3.4$\times$. Our method outperforms the strongest baseline, SVDQuant, by 2.5–8.7 percentage points. In real-world deployment on a Unitree G1 humanoid and a UR3 bimanual robot, our quantized Fast-WAM and ImageWAM reach 56.0% and 76.0% average success rate, 12.8 and 17.6 percentage points above SVDQuant.