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arXiv · 2509.16756

Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees

Yuchen Liang·Yingbin Liang·Lifeng Lai·Ness Shroff
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Abstract

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these, $τ$-leaping samplers have become particularly popular due to their theoretical and empirical success. However, existing theoretical analyses of $τ$-leaping often rely on somewhat restrictive and difficult-to-verify regularity assumptions, and their convergence bounds contain quadratic dependence on the vocabulary size. In this work, we introduce a new analytical approach for discrete diffusion models that removes the need for such assumptions. For the standard $τ$-leaping method, we establish convergence guarantees in KL divergence that scale linearly with vocabulary size, improving upon prior results with quadratic dependence. Our approach is also more broadly applicable: it provides the first convergence guarantees for other widely used samplers, including the Euler method and Tweedie $τ$-leaping. Central to our approach is a novel technique based on differential inequalities, offering a more flexible alternative to the traditional Girsanov change-of-measure methods. This technique may also be of independent interest for the analysis of other stochastic processes.

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Yuchen Liang, Yingbin Liang, Lifeng Lai, Ness Shroff. 2025-10-31. Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees. https://arxiv.org/abs/2509.16756

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