Prior masked modeling motion generation methods predominantly study text-to-motion. We present DiMo, a discrete diffusion-style framework, which extends masked modeling to bidirectional text--motion understanding and generation. Unlike GPT-style autoregressive approaches that tokenize motion and decode sequentially, DiMo performs iterative masked token refinement, unifying Text-to-Motion (T2M), Motion-to-Text (M2T), and text-free Motion-to-Motion (M2M) within a single model. This decoding paradigm naturally enables a quality-latency trade-off at inference via the number of refinement steps. We further improve motion token fidelity with residual vector quantization (RVQ) and enhance alignment and controllability with Group Relative Policy Optimization (GRPO). Experiments on HumanML3D and KIT-ML show strong motion quality and competitive bidirectional understanding under a unified framework. In addition, we demonstrate model ability in text-free motion completion, text-guided motion prediction and motion caption correction without architectural change. Additional qualitative results are available on our project page: https://animotionlab.github.io/DiMo/.