提出离散扩散采样新算法，提升生成模型后验推断效率
Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spaces
- 引入离线策略训练技术，改进离散空间采样性能
- 在合成数据集上实现比现有方法更高采样精度
- 首次实现离散域数据到能量的薛定谔桥建模，适用于图像生成潜空间
从一个仅知归一化常数的分布 $p(x) /propto e^{-ar{E}(x)}$ 中采样是统计学中的重要且具有挑战性的问题。近年来，一类称为扩散采样器的可迁移采样算法兴起，能够高效快速地从非归一化密度中采样。这类算法在连续空间采样任务中已被广泛研究，但在离散空间中的应用仍处于起步阶段。尽管已有部分进展，但现有离散扩散采样器未能充分利用连续空间中的成熟思想。本文通过引入离散扩散采样器的离线策略训练技术，弥合这一差距。实验表明，该方法在既有和新设计的合成基准上显著提升了采样性能。进一步地，我们将离散扩散采样器推广至任意两分布间的桥接任务，首次提出离散域的数据到能量的薛定谔桥训练方法。最后，展示了所提扩散采样器在图像生成模型离散潜空间中实现无数据后验采样的应用。
原文摘要 · Abstract (English)
Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schrödinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.
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