Recent advances in motion diffusion models have enabled spatially controllable text-to-motion generation. However, despite achieving acceptable control precision, these models suffer from generation speed and fidelity limitations. To address these challenges, we propose ControlMM, a novel approach incorporating spatial control signals into the generative masked motion model. ControlMM achieves real-time, high-fidelity, and high-precision controllable motion generation simultaneously. Our approach introduces two key innovations. First, we propose masked consistency modeling, which ensures high-fidelity motion generation via random masking and reconstruction, while minimizing the inconsistency between the input control signals and the extracted control signals from the generated motion. To further enhance control precision, we introduce inference-time logit editing, which manipulates the predicted conditional motion distribution so that the generated motion, sampled from the adjusted distribution, closely adheres to the input control signals. During inference, ControlMM enables parallel and iterative decoding of multiple motion tokens, allowing for high-speed motion generation. Extensive experiments show that, compared to the state of the art, ControlMM delivers superior results in motion quality, with better FID scores (0.061 vs 0.271), and higher control precision (average error 0.0091 vs 0.0108). ControlMM generates motions 20 times faster than diffusion-based methods. Additionally, ControlMM unlocks diverse applications such as any joint any frame control, body part timeline control, and obstacle avoidance. Video visualization can be found at https://exitudio.github.io/ControlMM-page
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