解决扩散采样中多模态模式坍塌问题，通过路径逐步逼近目标分布。
Proximal Diffusion Neural Sampler
- 用路径空间的近端点法分解采样学习为渐进子问题。
- 在分子动力学等复杂任务中实现稳定采样，避免模式丢失。
- 适合需要高多样性采样的科学计算与生成建模场景。
基于扩散的神经采样器用于从非归一化目标分布中采样，可视为路径测度上的随机最优控制问题。当目标分布具有多个模式且模式间存在显著屏障时，训练神经采样器可能引发模式坍塌。本文提出近端扩散神经采样器（PDNS），通过在路径测度空间上使用近端点法求解该随机最优控制问题，将学习过程分解为一系列更简单的子问题，逐步构建接近目标分布的路径，促进模式间的充分探索。为实现高效实用，每个近端步骤采用近端加权去噪交叉熵（WDCE）目标函数。在连续与离散采样任务上，包括分子动力学和统计物理中的挑战性场景，实验验证了PDNS的有效性与鲁棒性。代码已开源。
原文摘要 · Abstract (English)
The task of learning a diffusion-based neural sampler for drawing samples from an unnormalized target distribution can be viewed as a stochastic optimal control problem on path measures. However, the training of neural samplers can be challenging when the target distribution is multimodal with significant barriers separating the modes, potentially leading to mode collapse. We propose a framework named Proximal Diffusion Neural Sampler (PDNS) that addresses these challenges by tackling the stochastic optimal control problem via proximal point method on the space of path measures. PDNS decomposes the learning process into a series of simpler subproblems that create a path gradually approaching the desired distribution. This staged procedure traces a progressively refined path to the desired distribution and promotes thorough exploration across modes. For a practical and efficient realization, we instantiate each proximal step with a proximal weighted denoising cross-entropy (WDCE) objective. We demonstrate the effectiveness and robustness of PDNS through extensive experiments on both continuous and discrete sampling tasks, including challenging scenarios in molecular dynamics and statistical physics. Our code is available at https://github.com/AlexandreGUO2001/PDNS.
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