不依赖优化与扩散过程，用扰动理论重构生成模型。
Optimization-Free Diffusion Model -- A Perturbation Theory Approach
- 基于后向柯尔莫哥洛夫算子的特征基展开得分函数
- 将得分估计转为求解线性系统，避免迭代优化
- 在高维玻尔兹曼分布和真实数据集上验证有效
扩散模型作为生成建模的强大框架，通常依赖神经网络优化以通过前向SDE模拟估计得分函数。本文提出一种无需优化且无需前向SDE的新方法：通过对与扩散过程相关的后向柯尔莫哥洛夫算子的稀疏特征基展开得分函数，将得分估计转化为求解线性系统，从而避免了迭代优化和时变样本生成。我们运用扰动理论分析近似误差，并在高维玻尔兹曼分布及真实数据集上验证了该方法的有效性。
原文摘要 · Abstract (English)
Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is both optimization-free and forward SDE-free. By expanding the score function in a sparse set of eigenbasis of the backward Kolmogorov operator associated with the diffusion process, we reformulate score estimation as the solution to a linear system, avoiding iterative optimization and time-dependent sample generation. We analyze the approximation error using perturbation theory and demonstrate the effectiveness of our method on high-dimensional Boltzmann distributions and real-world datasets.
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