用物理信息神经网络提升扩散采样精度，尤其擅长处理分离成分的混合比例识别。
Diffusion-PINN Sampler
- 通过PINN求解对数密度的控制偏微分方程来估计反向SDE漂移项
- 在含孤立成分的目标分布上准确识别混合比例，采样误差显著降低
- 适用于高维复杂分布采样，尤其适合需要精确混合比例的任务
扩散模型的成功激发了利用反向扩散过程进行采样的研究热潮。然而，仅从非归一化目标密度准确估计反向随机微分方程（SDE）的漂移项存在重大挑战，限制了现有方法达到顶尖性能。本文提出扩散-PINN采样器（DPS），一种新型基于扩散的采样算法，通过物理信息神经网络（PINN）求解底层SDE边际对数密度的控制偏微分方程，来估计漂移项。我们证明了对数密度近似误差可由PINN残差损失控制，从而建立DPS的收敛性保证。在多种采样任务上的实验表明，该方法有效，尤其在目标分布包含孤立成分时能准确识别混合比例。
原文摘要 · Abstract (English)
Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE) solely from the unnormalized target density poses significant challenges, hindering existing methods from achieving state-of-the-art performance. In this paper, we introduce the Diffusion-PINN Sampler (DPS), a novel diffusion-based sampling algorithm that estimates the drift term by solving the governing partial differential equation of the log-density of the underlying SDE marginals via physics-informed neural networks (PINN). We prove that the error of log-density approximation can be controlled by the PINN residual loss, enabling us to establish convergence guarantees of DPS. Experiments on a variety of sampling tasks demonstrate the effectiveness of our approach, particularly in accurately identifying mixing proportions when the target contains isolated components.
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