Human motion is inherently continuous and dynamic, posing significant challenges for generative models. While discrete generation methods are widely used, they suffer from limited expressiveness and frame-wise noise artifacts. In contrast, continuous approaches produce smoother, more natural motion but often struggle to adhere to conditioning signals due to high-dimensional complexity and limited training data. To resolve this 'discord' between discrete and continuous representations we introduce DisCoRD: Discrete Tokens to Continuous Motion via Rectified Flow Decoding, a novel method that leverages rectified flow to decode discrete motion tokens in the continuous, raw motion space. Our core idea is to frame token decoding as a conditional generation task, ensuring that DisCoRD captures fine-grained dynamics and achieves smoother, more natural motions. Compatible with any discrete-based framework, our method enhances naturalness without compromising faithfulness to the conditioning signals on diverse settings. Extensive evaluations demonstrate that DisCoRD achieves state-of-the-art performance, with FID of 0.032 on HumanML3D and 0.169 on KIT-ML. These results establish DisCoRD as a robust solution for bridging the divide between discrete efficiency and continuous realism. Project website: https://whwjdqls.github.io/discord-motion/