The rapid development of Diffusion Language Models (DLMs) raises concerns about watermarking for DLM-generated detection. However, existing sequential LLM watermarking cannot be directly applied to DLMs, as DLMs’ generation order is arbitrary. While emerging studies adapt biased LLM watermarking to DLMs by temporarily predicting the watermark prefix, they suffer from degraded quality and unstable watermarking due to bias accumulation and prediction errors. Besides, they cannot carry multi-bit watermarks. In this paper, we propose unbiased multi-bit watermarking for DLMs. We introduce a stability-aware constraint that allows watermarking only in stable contexts and a bit-controlled, unbiased modulation to preserve the original DLM output distribution, achieving stable watermarking with minimal quality impact. To enhance detection robustness, we design a Regret-based Remasking, which grants a “second chance” for unwatermarked tokens to be regenerated. It can seamlessly integrate into DLM inference with no added diffusion steps and latency. Experiments across DLMs and various tasks show that our scheme is effective, achieving superior generation quality compared to baselines while maintaining high detection accuracy and multi-bit capacity. Our code is available here https://github.com/iieSKLCSDsg/UMR.