标题： 超越分数：邻近扩散模型 显示英文标题

标题： Beyond Scores: Proximal Diffusion Models

摘要： 扩散模型迅速成为高维数据最流行和强大的生成模型之一。 使它们得以发展的关键见解是认识到，访问不同噪声水平下的得分——对数密度的梯度——可以通过正向离散化求解反向时间随机微分方程（SDE）来从数据分布中进行采样，并且流行的去噪器允许对这个得分进行无偏估计。 在本文中，我们证明了使用邻近映射代替得分对这些SDE进行另一种反向离散化，可以带来理论和实际的好处。 我们利用最近在邻近匹配方面的研究成果来学习对数密度的邻近算子，并据此开发了邻近扩散模型（ProxDM）。 理论上，我们证明了 $\widetilde{O}(d/\sqrt{\varepsilon})$ 步足够使所得离散化相对于KL散度生成一个 $\varepsilon$-准确的分布。 经验上，我们表明ProxDM的两种变体在仅几个采样步骤内相比传统的得分匹配方法实现了显著更快的收敛。 显示英文摘要

摘要： Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the log-density at different noise levels -- allows for sampling from data distributions by solving a reverse-time stochastic differential equation (SDE) via forward discretization, and that popular denoisers allow for unbiased estimators of this score. In this paper, we demonstrate that an alternative, backward discretization of these SDEs, using proximal maps in place of the score, leads to theoretical and practical benefits. We leverage recent results in proximal matching to learn proximal operators of the log-density and, with them, develop Proximal Diffusion Models (ProxDM). Theoretically, we prove that $\widetilde{O}(d/\sqrt{\varepsilon})$ steps suffice for the resulting discretization to generate an $\varepsilon$-accurate distribution w.r.t. the KL divergence. Empirically, we show that two variants of ProxDM achieve significantly faster convergence within just a few sampling steps compared to conventional score-matching methods.