用近端映射替代梯度，让扩散模型采样更快更准。
Beyond Scores: Proximal Diffusion Models
- 用近端映射替代传统得分估计，改进扩散模型采样路径。
- 理论证明只需 $\widetilde{O}(d/\sqrt{\varepsilon})$ 步即可达到 $\varepsilon$ 精度的分布逼近。
- 实验证明新方法在数步内收敛速度远超传统得分匹配方法。
扩散模型已成为高维数据生成中最流行且强大的模型之一。其核心思想是利用不同噪声水平下的得分（对数密度梯度）通过正向离散化反向随机微分方程实现从数据分布中采样，而常见去噪器可提供无偏得分估计。本文证明，采用反向离散化并以近端映射替代得分，能带来理论与实践优势。我们借助近端匹配的最新成果学习对数密度的近端算子，并据此提出近端扩散模型（ProxDM）。理论上，我们证明该离散化仅需 $\widetilde{O}(d/\sqrt{\varepsilon})$ 步即可在 KL 散度意义下生成 $\varepsilon$-准确的分布。实验表明，两种 ProxDM 变体在仅数步采样内即实现显著更快的收敛速度，优于传统得分匹配方法。
原文摘要 · Abstract (English)
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.
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