From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models

Problem
This paper addresses the inefficiency in sampling from uniform-rate discrete diffusion models, which often require numerous steps to generate a single sample. Existing acceleration techniques either necessitate additional training or exhibit slow mixing properties. The authors present a novel approach, termed Gibbs-Accelerated Discrete Diffusion (GADD), which does not require extra training beyond standard score estimation. This work is a preprint and has not yet undergone peer review.

Method
GADD introduces a Gibbs-based corrector that constructs Gibbs posterior likelihoods directly from the concrete score function. The method operates without additional training, leveraging the existing score estimation framework. The authors demonstrate that GADD achieves a sampling complexity of (\mathcal{O}(\mathrm{polylog} (\varepsilon^{-1}))), marking a significant advancement in the efficiency of sampling from uniform-rate discrete diffusion models. The theoretical foundation of GADD is built on an induction argument that tracks error propagation across predictor iterations, which is a departure from traditional methods that utilize the Girsanov change-of-measure technique. This framework may provide insights into predictor-corrector methodologies in discrete diffusion contexts.

Results
GADD was evaluated against standard baselines, including vanilla Euler methods and Continuous-Time Markov Chain (CTMC) correctors, across various tasks: synthetic data generation, zero-shot text sampling, and zero-shot conditional music generation. The results indicate that GADD consistently enhances sample quality and wall-clock efficiency. While specific numerical results are not detailed in the abstract, the authors claim that GADD achieves superior performance metrics compared to the aforementioned baselines, suggesting a significant improvement in both the quality of generated samples and the computational efficiency of the sampling process.

Limitations
The authors acknowledge that GADD’s performance may be contingent on the quality of the underlying score estimation. Additionally, while the method shows promise in various applications, its generalizability to other types of diffusion models or more complex data distributions remains to be fully explored. The reliance on the concrete score function may also limit the applicability of GADD to models where this structure is not present.

Why it matters
The introduction of GADD has important implications for the field of generative modeling, particularly in applications requiring efficient sampling from discrete distributions. By reducing the sampling complexity and improving efficiency without additional training, GADD could facilitate the deployment of discrete diffusion models in real-time applications, such as interactive text generation and music composition. Furthermore, the theoretical insights provided by the authors may inspire future research into more effective predictor-corrector frameworks, potentially leading to advancements in other areas of machine learning that utilize similar methodologies.

Authors: Yuchen Liang, Ness Shroff, Yingbin Liang
Source: arXiv:2605.27352
URL: https://arxiv.org/abs/2605.27352v1