标题： 扩散模型的似然匹配 显示英文标题

标题： Likelihood Matching for Diffusion Models

摘要： 我们提出了一种似然匹配方法，通过首先建立目标数据分布的似然与反向扩散样本路径上的似然之间的等价性，从而训练扩散模型。 为了高效计算反向样本似然，考虑了一个准似然，通过具有匹配的条件均值和协方差的高斯分布来近似每个反向转移密度。 通过最大化准似然来估计扩散生成的得分函数和海森矩阵函数，确保在每两个时间点之间的一阶和二阶过渡矩的一致匹配。 引入了一种随机采样器，以利用估计的得分和海森信息进行计算。 我们建立了准最大似然估计的一致性，并为所提出的采样器提供了非渐近收敛保证，量化了由于得分和海森估计、维度以及扩散步骤数量导致的近似误差率。 实证和模拟评估证明了所提出的似然匹配方法的有效性，并验证了理论结果。 显示英文摘要

摘要： We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion generation are estimated by maximizing the quasi-likelihood, ensuring a consistent matching of both the first two transitional moments between every two time points. A stochastic sampler is introduced to facilitate computation that leverages on both the estimated score and Hessian information. We establish consistency of the quasi-maximum likelihood estimation, and provide non-asymptotic convergence guarantees for the proposed sampler, quantifying the rates of the approximation errors due to the score and Hessian estimation, dimensionality, and the number of diffusion steps. Empirical and simulation evaluations demonstrate the effectiveness of the proposed Likelihood Matching and validate the theoretical results.