We propose a deterministic denoising algorithm for discrete-state diffusion models based on Markov chains. The generative reverse process is derandomized by introducing a variant of the herding algorithm with weakly chaotic dynamics, which induces deterministic discrete state transitions. Our approach is a direct replacement for the stochastic denoising process, requiring neither retraining nor continuous state embeddings. We demonstrate consistent improvements in both efficiency and sample quality on text and image generation tasks. Thus, this simple derandomization approach is expected to enhance the significance of discrete diffusion in generative modeling. Furthermore, our results reveal that deterministic reverse processes, well established in continuous diffusion, can also be effective in discrete state spaces.

翻译：我们提出了一种基于马尔可夫链的离散状态扩散模型的确定性去噪算法。通过引入一种具有弱混沌动力学的放牧算法变体，该算法诱导确定性的离散状态转移，从而对生成式逆向过程进行去随机化。我们的方法是随机去噪过程的直接替代方案，既不需要重新训练，也不需要连续状态嵌入。我们在文本和图像生成任务上证明了其在效率和样本质量方面的一致改进。因此，这种简单的去随机化方法有望增强离散扩散在生成式建模中的重要性。此外，我们的结果表明，在连续扩散中已得到充分确立的确定性逆向过程，在离散状态空间中同样可以行之有效。