We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

翻译：我们为用于扩散生成建模的确定性采样器开发了一个非渐近分析框架。近期多项工作利用Girsanov定理及插值论证的链式法则变体对随机采样器进行了分析。然而，这些方法应用于确定性采样器时会产生无效的边界。我们为确定性采样提供了新的操作解释：沿概率流ODE的一步可分解为两步：1）恢复步骤，在无穷小前时刻对条件对数似然执行梯度上升；2）退化步骤，使用指向当前迭代的噪声执行正向过程。该视角使我们能够将去噪扩散隐式模型推广至一般的非线性正向过程。我们进一步在数据分布的温和条件下，为这类采样器建立了首个多项式收敛边界。