In the visual generative area, discrete diffusion models are gaining traction for their efficiency and compatibility. However, pioneered attempts still fall behind their continuous counterparts, which we attribute to noise (absorbing state) design and sampling heuristics. In this study, we propose a rehashing noise approach for discrete diffusion transformer (termed ReDDiT), with the aim to extend absorbing states and improve expressive capacity of discrete diffusion models. ReDDiT enriches the potential paths that latent variables traverse during training with randomized multi-index corruption. The derived rehash sampler, which reverses the randomized absorbing paths, guarantees high diversity and low discrepancy of the generation process. These reformulations lead to more consistent and competitive generation quality, mitigating the need for heavily tuned randomness. Experiments show that ReDDiT significantly outperforms the baseline model (reducing gFID from 6.18 to 1.61) and is on par with the continuous counterparts.