提出可扩展且稳定的扩散采样新方法，解决现有方法的收敛与模式崩溃问题。
Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
- 基于固定点迭代思想，统一现有匹配方法并设计新目标函数。
- 在高维分子数据上实现前所未有的采样规模，保持模式多样性。
- 适合需要稳定大规模采样且关注分布保真的研究者使用。
通过扩散模型从非归一化密度中采样已成为一种强大范式。尽管近期采用最小二乘‘匹配’目标的方法提升了可扩展性，但通常需在先验分布限制或不稳定的优化方案间做出权衡。本文将这些方法视为基于Nelson关系的固定点迭代特例，提出新的桥接匹配采样器（Bridge Matching Sampler, BMS）。该方法通过单一可扩展、稳定的损失函数学习任意先验与目标分布间的随机传输映射。此外，引入阻尼变体，结合正则化项以缓解模式坍塌并进一步稳定训练。实验表明，本方法可在复杂合成分布和高维分子基准上实现前所未有的采样规模，同时保持模式多样性，达到当前最优性能。
原文摘要 · Abstract (English)
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations, called Bridge Matching Sampler (BMS). Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse and further stabilize training. Empirically, we demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.
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