提出基于马尔可夫模型的离散扩散生成方法，理论严谨且性能优越。
Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptions
- 在比特空间构建连续时间马尔可夫链进行去噪，逆转过程由离散得分函数调控。
- 在伯努利和二值MNIST数据上实现与顶尖方法相当的生成效果。
- 理论收敛性证明仅依赖最小假设，适合追求理论可靠性的研究者。
本文提出离散马尔可夫概率模型（DMPMs），一种用于离散数据生成的新颖离散扩散算法。该算法在比特空间中运行，去噪过程为连续时间马尔可夫链，以均匀随机方式翻转标签。逆向过程同样是跳跃过程，其强度由经典得分函数的离散类比决定，关键证明表明该强度即为前向过程某函数的条件期望，体现与得分生成模型的理论一致性。我们在最小假设下建立了算法的收敛界，确保鲁棒性与高效性，并在低维伯努利分布数据集和高维二值MNIST数据上验证了性能。实验结果表明，该方法在生成离散结构方面表现优异，达到当前最优水平。本工作连接了理论基础与实际应用，推动了有效且理论严谨的离散生成建模发展。
原文摘要 · Abstract (English)
This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain that flips labels uniformly at random. The time-reversal process, like the forward noise process, is a jump process with its intensity governed by a discrete analogue of the classical score function. Crucially, this intensity is proven to be the conditional expectation of a function of the forward process, underlining theoretical alignment with score-based generative models. We establish convergence bounds for the algorithm under minimal assumptions, ensuring robustness and efficiency, which we demonstrate through experiments on low-dimensional Bernoulli-distributed datasets and high-dimensional binary MNIST data. The results highlight competitive performance in generating discrete structures compared to the state-of-the-art. This work bridges theoretical foundations and practical applications, advancing the development of effective and theoretically grounded discrete generative modeling.
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